WHEN POLICE receive allegations about the conduct of a chief or a mayor--however false they may turn out to be--to whom should they go for an investigation? This, as much as a finding of no substance to allegations received by police about Mayor Barry, was what was important about reporter Athelia Knight's recent account of her two-month inquiry into the matter. Having noted the smear quality of some reactions to the unsubstantiated charges, we now come back to this story not to harp on false information but to look at how it was handled by authorities.

Miss Knight's detailed account points up differences of opinion about police department procedures for following up such sensitive allegations. Inspector Fred Raines, who was head of the department's intelligence unit, believes there should have been at least a follow-up investigation by police or an outside agency. According to the inspector, he advised Police Chief Maurice Turner in January 1982 of one allegation against the mayor. But the chief has denied that Inspector Raines informed him about this. In March, after sending a detective to check into some more charges, Inspector Raines says, he made a report of interviews with three people.

The inspector says he also called someone at the FBI for advice and, following a suggestion, went to the Justice Department, where a few days later he was informed that the Justice Department did not usually enter such cases. It was then, says Inspector Raines, that he told Chief Turner about the later allegations. When Inspector Raines received a fourth allegation last fall, he says, he went to Assistant Chief Marty Tapscott and then to Chief Turner. But Chief Turner has said he knows nothing about this fourth report.

What the chief did say was that he might have to demote Inspector Raines for going to Justice without informing his superiors. And since then, Inspector Raines has been transferred to night duty.

What we are left with at this point, then, are discrepancies in these two reports--and no clear policy for any other officer who might come upon sensitive charges involving his superiors. "Going up the chain of command" is fine when no link is bent--but when a superior seems not to be responding, the police officer should be able to go to a U.S. attorney's office, a judge or somebody in a position to investigate. These are not likely to be frivolous approaches, since most officers would think twice about spreading serious charges about their superiors.

Having addressed the allegations, Mayor Barry now should set this other record straight as well-- and set forth a clear policy.