State police said the incident remains under criminal investigation and is also the subject of an internal affairs inquiry. Officials have not released details about the reasons for the suspensions or said which trooper was connected to the accused visitor.

The case centers on temporary housing used by a small number of troopers assigned to the island during the summer. The accommodations are in a building separate from the State Police barracks on Temahigan Avenue.

Edward J. Brown, 27, a Boston Public Schools employee, was arrested on a rape charge in connection with the case. He pleaded not guilty in Edgartown District Court, was ordered held on $10,000 bail and is due back in court Dec. 3. His attorney, Anthony Ellison, has said Brown maintains his innocence.

Oak Bluffs police have said the alleged assault occurred Aug. 15. State police Colonel Geoffrey Noble called the allegations “deeply troubling” and said the department is cooperating with the criminal investigation while reviewing its policies, visitor-approval procedures and compliance requirements.

After the incident, Noble barred overnight guests at seasonal trooper housing on Martha’s Vineyard and Nantucket. He also ordered a written policy requiring advance approval from a barracks commander for visitors entering nonpublic areas of State Police property, where visitors must be accompanied at all times.