Prince George's County Executive Lawrence J. Hogan has asked Police Chief John W. Rhodes for a detailed report on security at the Capital Centre to help him determine whether county police should continue regular patrols there.

Hogan asked Rhoads for the report Tuesday when they met for the first time since Hogan defeated Winfield M. Kelly Jr. in the November elections.

County police have patrolled the perimeter areas of the sports arena ever since the building opened five years ago. Their presence has been a subject of controversy since then because the arena is privately owned but does not pay for the police who work there.

"We definitely want to take a closer look at the situation over there before we make any decisions one way or the other," said Hogan's aide, Robert T. Ennis. "It may well be that we want to put less people over there or possibly not have any people there at all."

Hogan ran his campaign on a budget-cutting platform and has been under pressure from the police union to eliminate the Capital Centre patrols.

"Why should the county pay for security out there?" union president Laney Hester complained. "If a county high school wants a patrolman to work at a football game or something, the school board has to pay for that officer's overtime. Why should a nongovernment organization get its security for free?"

Rhoads has defended the Capital Centre patrols in the past, saying police are needed wherever a large crowd gathers. "If something happens it's easier to have a group of individuals there than to come in after the fact, to mobilize our street forces and then move in en masse. We would be at a tactical disadvantage."

The county police -- usually anywhere from 5 to 25 officers, are assigned, depending on the event -- patrol the parking lots, access roads and the areas leading into the building itself.

As many as a dozen county park police patrol the area around the arena on horseback. A private security patrol works inside the arena itself. The cost to the county for police protection at the 20,000-seat arena has been estimated at about $120,000 annually.

The Capital Centre contingent has been reduced during the past year, with heavy concentrations of police working only on nights when rock concerts are scheduled. County police spokesman John Hoxie said the department is now in the process of reorganizing the patrols again and is likely to reduce again the number of men assigned there.

"I haven't made a decision one way or the other about it yet," Hogan said yesterday. "I've just asked Chief Rhoads to give me an assessment of the situation."

During the arena's inception, construction and operation, it has been closely identified with the Democratic political and government leadership of the county.

Its attorney is Peter F. O'Malley, former leader of the county's Democratic Party while owner Abe Pollin is a Democratic fund-raiser.

But in spite of that image, Capital Centre remains a private, profit-making institution. Hogan is expected to decide early next year whether to curtail or cancel the police patrols on the arena grounds.