The Finance Committee of the Annapolis City Council, acting against the advice of Mayor Richard Hillman, has opened the way to a bidding war for rights to produce the immensely popular boat shows held here in the fall at the City Dock.

The committee, responding to accusations that the city is being shortchanged on its rental fee, will draw up bid specifications and accept proposals for shows starting in 1986, committee member John Hammond said.

The U.S. sailboat and powerboat shows have been operating here every October since 1970, when local entrepreneurs Peter Carroll and Jerry Wood hatched the idea of in-the-water displays, a scheme so successful that it has since been copied around the world.

In recent years the shows, held over two weeks, have drawn tens of thousands of visitors, at up to $6.50 a person.

Carroll said annual profits are more than $800,000.

In 1976 Carroll sold out his half and agreed to a clause barring him from producing shows here until 1986.

Now he wants back in and recently advised the council he would apply for the right to produce the 1986 to 1990 shows.

Hillman, saying he is happy with Wood's management and with the financial bonuses the city enjoys from the boaters the shows draw, told Carroll by letter he would recommend against altering "the city's positive relationship" with Wood.

He added in an interview: "Something separates this show from all others and we don't want to play around with success. I'd rather deal with the issue of what is a fair rental" from Wood than endanger the show by offering it to someone new.

"If it was a choice between doing something that could cause the show to go to ruin or giving it away for free to Wood , I'd do the latter," Hillman said, because of the benefits it provides the city.

Carroll said Wood pays too little to use the dock and that he would do better for the city. "This guy Hillman fights so hard for every nickel of tax money. Here you have one asset that's worth a lot of money and he talks about giving it away," Carroll said. "It stinks to high heaven."

Carroll said he would offer $1 million to the city for the five-year lease he seeks, "and that's just my starting offer."

Wood is obliged to pay $142,000 in 1985 and has said that amount would increase "substantially" in contract proposals for 1986-87.

The Finance Committee heard Carroll's arguments Wednesday and decided to draw up specifications for competitive bidding.

"What we decided," said John Hammond, "is that if someone else comes forward we'll listen to what he has to offer.

"That doesn't mean we're dissatisfied" with Wood's operation, he said. "As managers of the public interest we can't rule out someone who comes forward with another proposal." Added Hammond, "Mr. Wood has done a very fine job. Other proposals are going to have very tough competition."

Carroll maintains that Wood is making a killing.

But Wood, who will not disclose income and attendance figures from the shows, said, "If the shows make $800,000, why did he sell out his half for $500,000?"

Hillman said he believes that opening the show to competitive bids "will not change the ultimate decision."

He said Finance Committee members are "wasting their time, but it's theirs to waste."

As to the prospect of a shower of new applications to stage the lucrative shows, both Carroll and Wood said the complicated mechanics of production make that unlikely.

Wood has a leg up, since he has the most costly materials--the hundreds of yards of temporary docks--already in hand.