Last spring the Butler County, Ky., High School Band gave a Sunday afternoon concert at the school, which was attended by the local congressman, Rep. Carroll Hubbard Jr. (D-Ky.). After the concert, he was introduced and spoke a few words of praise to the band and their families.

"I officially invite you to march in the inaugural parade," is how band director Charles Black of Morgantown remembers Hubbard's words. Indeed, that's how they all remembered it - all 90 members of the band, the parents' boosters club - everyone, in fact, except Rep. Hubbard.

The band started immediately to raise the $10,000 to come to Washington. They borrowed trucks from the state enviromental agency to pick up junk in the county and sell them for scrap, a project that netted $7,000. They sold calenders, and the school board donated the rest.

They made a $300 deposit on motel rooms in Washington, and were starting to look into bus rental when they got the word from Rep. Hubbard Dec. 16: Despite his efforts, they were not to be invited to play in the inaugural parade. Instead, the chairman of the Carter campaign in Kentucky had invited his hometown band from Henderson County.

"Carter's campaigns started in Henderson, and it's traditional for the state chairman to choose his hometown band," said state Carter chairman Dale Sights. "Anyway, Hubbard never contacted me about Butler County."

Dallas Embry, president of the Butler band boosters, reflected the disappointment of the entire group. "Would we have worked all year if we'd had any doubt we were going?" he said.

Hubbard could not be reached for comment.

The politics of getting into an inaugural parade vary from state to state. The inaugural committee here simply told every state that its governor could nominate a limit of two units, of which the second choice had to be a float. The first choice could be a band, an equestrian or a marching unit.

In addition, the inaugural committee accepted floats from a few other organizations including the AFL-CIO, the Americus-Sumter County (Ga.) Chamber of Commerce, and the President's Council of Physical Fitness, which will have people jumping on a trampoline attached to its float. The Americus, Ga., High School Band was also permitted to participate because Predient-elect Jimmy Carter asked for them, and Minnesota gets to send two bands, because their native son Walter Mondale is being installed as vice president.

Some 10 other bands were recruited as well to stand along the parade route and play before the parade. Two bag-pipe groups were chosen because there weren't any bagpipers elsewhere in the parade, and an inner-city group from a Chicago vocational school was picked because there weren't any other inner-city bands. "They usually can't afford to pay their own way here," said band coordinator Sally Regal.

In some states, the governor promptly turned the task of choosing the parade entries over to an aide. The Departments of Public Inuformation got the task in Kentucky; the governor's assistant for economic and energy development got it in California.

The guidelines sent by the inaugural committee initially said that the float themes should be in keeping with the inaugural theme: "A new spirit, a new commitment, a new America," and that they should preferably be in earth tones and represent something about the different approach of the Carter administration.

Thus parade viewers will see among the 33 floats, 55 bands, 25 military units, assorted fire engines and horse groups the following:

The producer of "The Godfather" on the Georgia state float, Col. Harlan ("Kentucky Fried Chicken") Sanders in the Kentucky float, the Peanut Brigade carrying a giant peanut shaped balloon, a band from Texas that can do 220 shuffle steps a minute and has a blind trumpeter, a covered wagon from Indiana, and four "alternative vehicles" from the Energy Research and Development Administration.

Then there was Connecticut, whose float was rejected because it didn't fit the theme of the inauguration: "A New Spirit, A New Commitment, A New America." The float was actually one that had been used before on Memorial Day, and it depicted on replica of the Statue of Liberty emerging from a quartered globe along with a Liberty Bell and an American Eagle.

The problem, according to Maj. Gen. John F. Freund of Conneticut's National Guard Armory, is that the first round of instructions he received from the inaugural committee said only that the float theme should reflect the inaugural theme as "a reaffirmation of values that made our nation strong in the past."

A later directive, saying that the floats with a "Bicentennial theme" would be discouraged, and that the float should reflect "the unique nature of the people of the state," unfortunately did not arrive in Conneticut until after the float was in the process of being reassembled. In fact, Freund said he never did receive those directions until he got the phone call a week ago telling him the float was rejected.

"I realize the people at the committee are under tremendous pressure and it's possible to drop the ball every now and then," Freund said.

The state is sending two historic marching bands who have been coming to inaugural parades since 1929, he added.

Only 23 states are sending floats: many were contracted out to professional firms in this area and are being assembled here in a warehouse in the Navy Yard. Others are winding their ways to Washington through various snowstorms and will get finishing touches in the warehouse early inauguration day. Every state and territory except Puerto Rico is sending either a float or a band.

Each float committee was asked to have people standing on the float: preferably people who represented something about the state or the organization.

California is relying largely on Capitol Hill staffers of Congressmen from the state - friends and acquaintances of the woman in the Washington-based California state office who is recruiting them. Col. Sanders will be among the costumed Kentucky jockeys, pioneers, coal miners and antebellum outfitted riders because "he's sort of a folk hero in Kentucky." said Ed Graves of Sen. Walter Huddleston's office (D-Ky.). "People get him to come to parades all the time, he likes to be in them. He's probably the best known person in Kentucky."

Most of the other people on Kentucky's float will be from that state's congressmen's offices on Capitol Hill - which can also lead to problems. One chap who is a portray Daniel Boone brought his antique musket to work one day and was stopped by the Capitol Police and interrogated for several hours.

"He said it was pretty rough," said Faith Miller in Huddleston's office. There will be no guns, antique, fake or otherwise on parade floats, it has been decided.

Georgia's float is designed to basically advertise to the world how great Georgia is. "We want to attract business to Georgia as well as honor the President and our state," said Tommy Dortch, associate director of the state Democratic Party. "It's a wonderful place to live, work or play."

One baseball hero Hank Aaron's sons will be on the float representing sports; Miss Georgia will represent beauty; Miss Georgia Holiday will represent tourism; a "pretty" speech pathology teacher (and member of the state Democratic Committee) will represent education: a prize-winning cabinet maker will represent the "hard-hat guys" a 23-year-old farmer will represent farming, and "The Godfather" producer Albert S. Ruddy will represent the film industry, Dortch said.

Ruddy produced "The Longest Yard" in Georgia and Dortch said the state has benefited from $4 billion in revenues from that and over 70 other movies and TV shows filmed there.

"Tray" Polk is the farmer. His father is Steve Polk, Jr. (Tray is Steve III), who is in charge of all state buildings, including the governor's mansion. Tray, who has been leasing his 800 acre dairy farm but is about to buy his own 268 acres. "God-willing" is a particularly apt choice. It was actuall Jimmy Carter who got him started in dairy farming.

"The Georgia Dairymen gave Gov, Carter a Holstein heifer calf," he said. "He carried it to the governor's mansion but after six or seven weeks he called my daddy and said he thought the calf should be somewhere else besides the governor's mansion. He didn't think it was right to sell it, so he told daddy to take it out to me.

"We named it Rosie after Mrs. Carter, and she got me started in the dairy business. She's such a pretty heifer . . . you know she's different from any of 'em. She's had two bull calves. One man offered me $700 for her."

Washington, D.C. has chosen the most complicated way of choosing float riders, judging from the way other states have done it.

According to Dr. William C. Ramsey, director of the city's Department of Recreation which has been given the responsibility for the float, the riders will be chosen from nominations from each of the city's eight wards.

Five on the float are each to represent a different ethnic group from the city: black, white, Oriental, American Indian, and hispanic. In addition, there will be a senior citizen. So each ward, through its ward recreation manager and its City Council member, must nominate six persons, one from each category, who will then be judged and selected by a panel consisting of the ward recreation managers.

Getting money to get the various parade bands and floats riders to Washington and feed and house them here has been a major project in states across the nation.

On band picked oranges during the Christmas vacation. The Carson City, Nev., High School Marching Band solicited (and got) contributions from gambling casinos. Elsewhere, city councils voted appropriations, booster clubs held bake sales, car washes, dance marathons and "slave auctions." In Guam, which is sending both a band and a float because "we are so proud, as the only place in the country to have seen warfare on our land, to be part of America," community contributions are financing the entire trip, according to a spokesman.

For at least one band, the trip to Washington is the culmination of a three-year project to play in the nation's capitol.

The Rancho Cotate Band of Robert Park, Calif., started pressuring their governor's office a year ago for a place in the inaugural parade. Band director Jim Wright said he expected the group would have to compete for the position, but they went ahead and started raising the $42,000 it's costing to fly the 118 players and chaperones to Washington. Wright has worked "time and half" on the project since April.

Finally they got the word from Sacremento. Wright said: the band was chosen because no other high school bands who could afford to pay their own way wanted to go.

The group's hosts here will be members of the Edison High School Band in Fairfax County, whose director is an old Army buddy of Wright. Members of the Fairfax band are housing those from California.

"This is the culmination of a three-year dream," Wright said. "We plan to see everything in Washington."