Alexandria Mayor Charles E. Beatley Jr. yesterday issued a sharp protest to nearby Prince George's County, accusing its police recruiters of trying to lure black city policemen on their beats to better-paying jobs across the Potomac.

In a strongly worded letter to Prince George's County Executive Lawrence J. Hogan, Beatley threatened to cut off "intergovernmental cooperation," and warned Hogan not to look for "shortcuts in getting competent people on board."

"It's piracy on the highways," said one top Alexandria police officer. "We've got three black officers in the last two years because of the recruiters. If they worked for the Amry you wouldn't have to even consider restoring the draft."

Alexandria officials yesterday cited the case of one black officer who, they said, was approached by a Prince George's recruiter while the patrolman was at the scene of an accident, and asked if he would consider switching to the Prince George's force. The officer declined.

An aide to Hogan said yesterday the county executive has not received the letter and could not comment.

But the aide, Stephanie Bolick, added, "It's important to remember that we didn't kidnap anyone." She quoted Hogan as saying that the county police force, often criticized for poor relations with blacks in the past, "tries to attract the best possible candidates."

Other police departments in the Washington metropolitan area said yesterday they were either unaware or unsure of whether Prince George's recruiting efforts have extended to their jurisdictions."I know they've been here, but I don't know how or when," said a spokesman for the Fairfax County police force.

Prince George's, spurred by a 1976 Justice Department hiring discrimination suit, has sharply increased the number of black police recruits in recent year. The suit, which was dropped in 1979, alleged that the average yearly incoming police class from 1970 to 1976 was only 3 percent black, although the county's population was 25 percent black.

Today, half of each new police class is back and the department as a whole is 11 percent black, according to county police officials, who acknowledged yesterday they have an "aggressive" minority recruiting policy.

"Well, I don't know if we ever had a recruiter talk to an Alexandria officer while he was at work," said deputy county police chief Rice Turner. "But if he did, I wouldn't have any problem with it. What we do isn't unethical. We tell people what we have to offer and if they want to join us, then fine."

It is not fine with Alexandria Police Chief Charles T. Strobel, who said he found attempts by Prince George's to "steal" black officers definitely unethical.

"If an officer leaves of his own volition, then that's the way the cookie crumbles," Strobel said. "But I'm very concerned when they send recruiters in."

Three black Alexandria officers have left to go to work for Prince George's in the past two years, and the city has lost another 25 for a variety of reasons, including pay, officials said.

The 228-member Alexandria force is 11 percent black, and the loss of the 28 officers has made it impossible for the city to increase that percentage, acording to Strobel. About one-third of Alexandria's population is black.

Among the attractions offered by Prince George's is starting salary of $14,726, almost $1,000 more than that in Alexandria. County officers also are allowed to drive police cruisers home from work, which was cited as an important factor by several police officers interviewed yesterday.

The county also offers a 10 percent pay increase to officers who have completed college, plus better retirement benefits than Alexandria's.

"We have a hard time matching their offer," Strobel said.

Attempts to reach Prince George's two full-time police recruiters were unsuccessful. "They're both out on the street recruiting," said a department spokesman.