Prince George's County Executive Lawrence J. Hogan has asked Maryland State Police to investigate allegations that a group of county police detectives operated a "death squad" in 1967.

Hogan's request was made after the Justice Department formally rejected a request Hogan made on Feb. 12 that the FBI investigate reports contained in The Washington Post last month.

The Post quoted a former detective and a former police informant as saying that police arranged a robbery of a convenience store, lured two teen-agers into committing the crime and then shot and killed one of them.

Hogan this week also asked Prince George's State's Attorney Arthur A. Marshall to "present the facts to the grand jury." Marshall said yesterday he has advised the grand jury that it would be inapropriate for his office to investigate since he was the prosecutor in 1967 and "cecause I believe the allegations are completely without substance."

Marshall said he would cooperate with the state police "if they feel an investigation is warranted."

"I still feel it is important that an impartial third party investigate these allegations," Hogan said yesterday. Col. Tom Smith, head of the state police, could not be reached for comment.

Hogan sent a copy of his letter to Maryland Attorney General Stephen Sachs, who agreed that an investigation should be conducted. Sachs is legal adviser to the state police.