Twenty-eight House Democrats regularly broke with their party's leadership and voted with the Reagan administration on crucial tax and budget proposals during the 97th Congress, according to a study released yesterday by the lobbying group Public Citizen.

The study of voting records was sent to newly elected members of Congress by Public Citizen's president, Joan Claybrook, along with a letter noting that some of the 28 Democrats who ignored the party line hold key committee positions. Some committee assignments will be voted on next week in preparation for the 98th Congress; party loyalty could be an issue in those votes.

The Public Citizen study closely reflects findings of an internal analysis of 31 key votes by the House Democratic leadership, which sought to determine which members deviated from the party line most often.

Reps. Larry McDonald (Ga.), G.V. (Sonny) Montgomery (Miss.), Phil Gramm (Tex.) and Marvin Leath (Tex.) were the most frequent offenders in both studies.

"Half of these critical congressional decisions affecting American families all over the nation were determined in favor of the Reagan administration by 28 or fewer votes during the 97th Congress," said Claybrook. "Ten of these 28 members are in key party posts, as committee chairmen, subcommittee chairmen, or members of the Democratic Steering and Policy Committee."

House Veterans' Affairs Committee chairman Montgomery voted against Democratic policies on all 12 votes on the Public Citizen list. Two subcommittee chairmen, Leath on a Veterans' Affairs panel and Andy Ireland (Fla.) of a Small Business unit, also voted against their party every time.

The 12 votes used by Public Citizen, whose founder was Ralph Nader, included votes on the May, 1981, budget resolution; tax cuts proposed in July, 1981; the first budget resolution in May, 1982; the nuclear arms freeze in August, 1982; the balanced-budget amendment in October, 1982, and the amendment to delete funding for procurement of five MX missiles earlier this month.

In addition to Montgomery, Leath and Ireland, Gramm and Reps. Richard C. Shelby (Ala.) and Charles W. Stenholm (Tex.) voted with the president all 12 times.

The other Democrats who voted with Reagan more than half the time on key votes were: Doug Barnard Jr. (Ga.), 10 times; Charles E. Bennett (Fla.), 7; John B. Breaux (La.), 11; Beverly B. Byron (Md.), 9; William V. Chappell Jr. (Fla.), 9; Robert W. Daniel Jr. (Va.), 10; Roy Dyson (Md.), 8; Glenn English (Okla.), 7; Ralph Hall M. (Tex.), 10; Sam B. Hall Jr. (Tex.), 11; Charles Hatcher (Ga.), 7; Jack Hightower (Tex.), 10; Thomas J. (Jerry) Huckaby (La.), 9; Earl Hutto (Fla.), 11; Dave McCurdy (Okla.), 8; Larry McDonald (Ga.), 11; Bill Nelson (Fla.), 8; Bill Nichols (Ala.), 11; Buddy Roemer (La.), 10; W.J. (Billy) Tauzin (La.), 11; and Charles Wilson (Tex.), 9 times.