The Prince George's County executive told the county police chief yesterday that the authorized police manpower level will be cut and several department functions will probably be eliminated and others reduced in size because of budget constraints, according to police sources.

County Executive Lawrence J. Hogan acknowledged that he told Chief John W. Rhoads that manpower will have to be cut, but refused to discuss specifics and said, "nothing is final."

"There's no question that the police are going to have to cut their budget, but I'm not asking them to cut it any more than any other department in the county," Hogan said last night. "Chief Rhoads was disturbed by some of the things our budget people recommended, so we are going to continue to talk about them."

Hogan said the reason for the cuts is TRIM, the voter-approved limit on property tax revenues approved last November and supported by Hogan.

Department sources said cuts tentatively planned include:

Cutting the authorized manpower of the department from 893 to 874 on July 1.

Eliminating the public information office, which consists of four people in the current budget.

Eliminating the traffic-safety division, which trains county police and municipal police within the county.

Cutting back the number of men in the Special Operation Division, which handles such things as demonstrations and hostage situations. and the number of dogs in the canine unit.

Cutting back the number of dispatchers in the communications division.

The police department now has 851 officers. Rhoads said last night that although his authorized strength would be 874, he expected attrition and retirements to keep the actual manpower closer to 840 or 850.

"I think I can handle the situation in this county with 874 men. That's why I requested that many," Rhoads said. "I know that if you look at the District of Columbia and see 4,300 policemen, you think we could use that many here.

"Ideally, we could have that many. I'd love to have a policeman on every corner. But we have to deal in economics and economics say we can't afford more than 874."

Rhoads said that while the budget would have to be cut this year, the cuts could be even more serious in 1981.

"I don't think we'll really know how big an effect TRIM will have until then," he said. "We may have to cut back further them. But that's 12 months away."

Rhoads said he did not know yet how much his budget would be cut. "I don't know dollar figures yet," he said. "We're still in preliminary discussions."

Members of the police rank-and-file complained last fall that the department was undermanned because it was operating under its authorized strength.

Rhoads said then that a new recruit class of 25 entering in February would solve that problem. Last night, he conceded that the new class would probably just maintain the status quo.

"The only reason why it looks like we're cutting the authorized manpower is because Kelly former county executive Winfield M. Kelly Jr. played games with the budget," Hogan said. "He had one figure down for the authorized manpower but wasn't budgeted for that many men."

Police union president Laney Hester saw the manpower cut as significant, however. "Crime continues to be the major problem in this county, and you aren't going to solve the problem with reduced manpower," he said. "I'm disappointed in the county executive and his budget advisers.

"The most basic service this government provides to the people is protection. I think to provide the basic services needed you need a minimum of 1,000 men. Baltimore County has about the same population as us and 1,100 policemen. Prince George's should do the same."