After Rex Heuermann was arrested last summer and then charged with murdering four women whose bodies were found in 2010 along Gilgo Beach on Long Island, prosecutors disclosed a barrage of details to support their case, including genetic evidence and sadistic porn sites they said Mr. Heuermann visited.

Now, with the trial still months away, the defense’s strategy is beginning to take shape. Mr. Heuermann’s lawyer, Michael J. Brown, has begun to float an alternate theory about the case: that the investigation into the murders was tainted years ago by the involvement of a now-disgraced Long Island police chief.

The chief, James Burke, who oversaw the investigation as head of the Suffolk County Police Department from 2012 to 2015, later became a symbol of police corruption and spent time in federal prison.

At a hearing last month following a procedural court appearance by Mr. Heuermann, Mr. Brown repeated his client’s claims of innocence. He also suggested that the real killer might have eluded arrest years ago when Mr. Burke was running the investigation.

Mr. Brown, a charismatic figure who arrives at court in a gleaming pickup truck, even suggested that Mr. Burke himself might have been involved in the four Gilgo killings, alluding to a fringe theory held by some followers of the case. Among the hundreds of leads turned over to him by prosecutors, Mr. Brown said, were “numerous” ones alluding to Mr. Burke’s involvement. Mr. Brown did not offer more details, and Mr. Burke is not a suspect in the case.

Mr. Brown, who has avoided doing interviews, has limited his public comments largely to damage control after court appearances.