Virginia is hard up for cash this year and many local governments are caught in the squeeze, but that didn't stop Norfolk Sen. Peter K. Babalas from introducing an appealing little bill that would freeze property tax rates throughout the state.

The bill's chances? "There's always a miracle . . . ," Babalas said. "I know the mood out there."

It is an election year out there for Virginia's 140 legislators, and the political art of introducing bills has peaked once again. More than 1,400 laws have been proposed in the first half of the six-week session, many of them tax-relief bills, get-tough-on-crime measures and other popular ideas with as little chance of becoming law as Babalas' bill.

At the same time, legislators are scrambling to sign their names to a winner so they can tell the voters they "co-patroned" bills that do become law.

Nora Squyres, a freshman delegate from Falls Church, drafted a bill to raise the legal drinking age to 21, this year's most popular issue. But Squyres, bowing to political reality, soon dropped her bill and--along with 34 other legislators--signed on to a similar administration-backed bill that has the best chance of passage. Altogether, Squyres is a co-patron of more than 50 proposals.

This is a year when legislators also are particularly eager to come to the aid of constituents back home. Fairfax Sen. Richard L. Saslaw, for instance, has introduced a bill to let physically and mentally handicapped people fish without a license, a request of a handicapped constituent, while Front Royal Del. Raymond R. (Andy) Guest Jr. introduced a measure exempting "acting pharmacists" from jury duty, the suggestion of a druggist in Berryville who had to close his store when he was called to the courthouse.

Probably no one tried to meet a more unusual request from a constituent than George P. Beard Jr., a delegate from Culpeper. Berniece Lee Oertel, a Lake of the Woods resident, was upset that funeral services had been held in the development's community building in October and is seeking a state law banning dead bodies in public dining areas.

Oertel had already asked several other public officials for help and finally had been told by the state Department of Health to seek legislative relief.

In a letter to Beard, she said she was told that the chances of the bill's passage were very good. "Such a bill," she wrote, "would fall in what the legislature calls the 'silly' category and such bills go through with little or no problem."

Beard had another bill in this year that arose from a particularly gruesome murder in Greene County. A mother was murdered by an intruder in front of her husband and children but because nothing was stolen in the course of the crime, prosecutors argued that they could not seek the death penalty. That prompted Beard to submit a bill that would cover the Greene County murder in Virginia's death penalty statute.

Like many other crime bills introduced here, Beard's death penalty bill was rejected early in the House Courts of Justice Committee, which, with more than 250 bills on its docket, is the most burdened committee in the General Assembly.

The Senate, too, is a barometer of the popularity of crime bills this year. The Senate Courts of Justice Committee last week was considering 84 bills. The Rehabilitation and Social Services Committee had eight.

Four legislators introduced bills to stiffen the penalties for assaulting police officers, while a fifth wanted to make it a crime to assault--or, to be precise, "willfully torture, torment, beat, kick, mutilate, injure, disable or otherwise mistreat"--a police dog or horse. The bill, introduced by Rocky Mount Sen. Virgil H. Goode Jr., also would make it a Class 1 misdemeanor "to interfere with the lawful performance of the duties of such dog or horse."

Last year the General Assembly passed a bill requiring safety seats for small children riding in cars. This year a bill was introduced to give tax credits for the purchase of such car seats, one of a dozen tax relief bills of various sorts introduced despite Virginia's $305 million projected deficit in this budget biennium.

"I don't think there's any realistic chance that these tax relief bills will pass, but it's an election year," said Alexandria Sen. Wiley F. Mitchell Jr. "There's no law against introducing bills, and they can go home and say they tried."

Prince William Del. Floyd C. Bagley, who like most Northern Virginia legislators represents a large number of veterans, introduced a bill to give tax breaks to military retirees, one of five proposals that would lend a hand to federal or military pensioners.

"This year I wouldn't think the prospects are particularly good," Bagley acknowledged. "But it's a response to the request of a large number of veterans, to indicate that there is an interest in keeping them here in Virginia, that the state is sympathetic to their requests."

Then there are the bills to give tax exemptions to popular organizations such as Outreach for Christ Inc. in Virginia Beach, the Rockingham County Fair Association Inc., the National Association of Ministers' Wives and Widows in Richmond or the Bose Audubon Center in Fairfax County. These exemptions are not always popular. "It's a hidden subsidy . . . and I just think it's bad public policy," said Mitchell.

Less controversial but also valuable for next fall's campaign are resolutions that would honor Confederate heroes John S. Mosby and Jeb Stuart, born 150 years ago this year; or a bill renaming Route 614 in far Southwest Virginia for A.P. Carter, who wrote "Will the Circle be Unbroken," "The Carter Family" and other country tunes.

Then there is the bill to set aside the third week in September for the Virginia Championship Applebutter Making Contest and the resolution requesting the federal government "to use all available remedies to eliminate the international drug trafficking industry."

Beard, a banker first elected in 1978, has seen his district lines change three times in three years and each year he has had a new set of constituents.

"My trouble is my personality," said Beard. "Anyone who's got a problem, I want to help them. I don't look at the overall problem, I look at the person involved."