U.S. District Judge Richard L. Williams refused yesterday to let federal prosecutors see secret testimony that Alexandria Police Chief Charles T. Strobel gave a state grand jury last year, saying they had not shown they need the material for Strobel's upcoming perjury trial.

Releasing the testimony also might "exacerbate what already appears to be a strained relationship" between state and federal authorities over the fact that both were investigating the city police department, Williams said at a crowded pretrial hearing in Alexandria.

The judge also denied several motions by Strobel's lawyers, clearing the way for his trial April 15 on charges of perjury and obstruction of justice.

Strobel, 48, was indicted Feb. 20 for allegedly lying to a federal grand jury about how he had handled reports concerning sexual misconduct by three policemen. The indictment contends he lied when he testified he did not remember receiving some of the reports.

Strobel, who has been police chief since 1977, has denied the charges.

A special state grand jury investigated Strobel and his department in early 1985, hearing many of the same witnesses who later testified before the federal grand jury that met throughout last year.

The judge said he had observed that this overlapping was "a matter of some sensitivity" and he would prefer to see "a healthy existence of comity" between the two agencies.

Williams called the request by Assistant U.S. Attorney Justin Williams to know what Strobel told the state grand jury a "typical wish-list type item" litigants pursue in the hope they will "find the nugget that will help their case." No charges were brought against Strobel by the state grand jury.

The judge also denied motions by Strobel attorneys Plato Cacheris and Larry S. Gondelman to dismiss four counts of the indictment on the grounds that they were repetitive and to throw out the indictment on the grounds that the federal grand jury was not authorized to investigate the allegations of sexual misconduct.