MINNEAPOLIS (AP) _ Health officials have criticized the disclosure by police that a murder victim believed to be a homosexual prostitute carried the AIDS virus.

''The police department should not be in the business of making decisions regarding the public health,'' Eric Engstrom, executive director the Minnesota AIDS Project, said Wednesday. ''This diminishes people's perception of the protection afforded such information.''

Michael Moen, a member of the state AIDS Task Force who is director of the Minnesota Health Department's division of disease prevention and health promotion, said there is concern about the effect of the police announcement on the health agency's credibility.

''A lot of people may not differentiate between the police and the health department,'' he said. ''To them, it's the government.''

Police, however, defended the disclosure, saying the public had a right to know that the victim, who they say was a gay prostitute and transvestite, was a carrier of the acquired immune deficiency syndrome virus.

''We have a social obligation to the community ... to alert anybody who might have had contact with him'' said Capt. Jack McCarthy.

The victim was identified as Floyd Thomas Olson, 30, a transient who was found strangled downtown Tuesday.

If police suspected Olson was a prostitute carrying the virus, ''why wasn't this matter brought to the Health Department earlier?'' Moen asked.

The lack of a systematic way to identify carriers of the disease and to determine if they are likely to spread it has left Moen and other health officials trying to deal on a case-by-case basis with AIDS carriers who won't cooperate, he said.

Before Wednesday, the Health Department had been aware of two instances of prostitutes who were AIDS carriers. In one case, the person's reluctance to cooperate with health officials resulted in the department getting a court order requiring her to cooperate and to refrain from ''high risk'' activities.

But there is no precedent for dealing with the case of an AIDS carrier whose ''high risk'' activities as a prostitute became known only after his murder, Moen said.

At this point, tracking sexual contacts the victim could have had is ''probably going to be pretty hard to do,'' Moen said.