Police in Upper Darby, Pennsylvania, say Simpson was arraigned Monday in a hospital and was being held on $1 million each on charges of auto theft and fleeing justice.
Federal prosecutors in Vermont also filed kidnapping charges against him.
A lawyer who has represented Simpson in the past did not immediately return a phone call seeking comment.
Federal prosecutors in Vermont have filed kidnapping charges against a man who authorities say forced a woman and her child into a car in New Hampshire, drove to Vermont and sexually assaulted the woman.
Everett Simpson was arrested in Pennsylvania after a manhunt and car chase on Sunday.
Authorities say the 41-year-old former St. Albans, Vermont, resident kidnapped the woman and 5-year-old child outside the Mall of New Hampshire in Manchester on Saturday and drove to Vermont. She told police he sexually assaulted her in a hotel room and then left.
Police say Simpson had escaped from an addiction treatment facility in Vermont days before. The woman told police that Simpson said he heard his wife was cheating on him and was looking for her so he could hurt her.
Authorities say a man forced a woman and her child into a car in New Hampshire, drove to Vermont, sexually assaulted the woman, and was apprehended in Pennsylvania after a manhunt and car chase.
Police say 41-year-old Everett Simpson faces extradition to Vermont and is expected to face federal charges related to car theft, kidnapping and sexual assault. Simpson was taken to a hospital.
Authorities say he kidnapped the woman and child outside the Mall of New Hampshire in Manchester on Saturday and drove to Vermont. When the woman and the child reached safety, they called the police.
A call was made to an attorney who has represented Simpson in the past, seeking comment.