A state trooper was relieved of duty early Friday after Stoughton police arrested him when he was found asleep in his personal car with the motor running and an open container of alcohol, officials said. Trooper Brian Simpkins, 39, was found in the parking lot of a Wendy’s restaurant at about 2:10 a.m. Friday, State Police said. “Stoughton officers found an open container of alcohol in his car and determined that he was impaired,’’ State Police said. Police arrested Simpkins on charges of operating under the influence of liquor, second offense, and having an open container of alcohol in a motor vehicle, the statement said. Simpkins joined the State Police in 2006. He was assigned to the State Police Barracks in Boston in the Lower Basin. He was ordered held in lieu of $1,000 cash bail at his arraignment Friday in Stoughton District Court. The State Police internal affairs section has opened an investigation. A hearing will be held next week at State Police headquarters on the trooper’s status.