Newsday says Detective Kenneth Ripp was concerned after interviewing David Laffer during an unrelated investigation.
Commissioner Richard Dormer says in a statement that "any information of acts of violence or illegal drug use" brought to Suffolk County police's attention would have been forwarded to the Pistol License Bureau.
Dormer says that would have prompted an immediate investigation and gun license suspension.
Dormer and pistol bureau officials declined interviews.
Laffer pleaded guilty to first-degree murder for the June bloodbath.
He says in a Newsday interview that the first shot was an accident. District Attorney Thomas Spota calls Laffer "an outrageous liar."