Murphy, the Republican chairman of the state Senate Judiciary Committee, is a foster and adoptive parent with a history of involvement in issues related to child-welfare, adoption and foster care issues. Police in Peoria, northwest of Phoenix, began the investigation June 22, The Arizona Republic reported Friday.
The investigation, in which state Child Protective Services are also taking part, followed allegations Murphy sexually abused children in his care, the newspaper said, citing police records it obtained through a public-records request.
Police said a teen had reported Murphy abused him repeatedly during a six-year period. Police reports indicate the teen also admitted he had inappropriate sexual contact with a child in the Peoria home where Murphy, 41, and his wife, Penny, 48, care for seven foster children.
The allegations resulted in police reopening a 2011 case in which a teen accused Murphy of fondling him daily during the course of a month, and offering to buy the boy a bicycle in exchange for keeping the alleged abuse quiet, the newspaper said.
Murphy has not been arrested and no charges have been filed in either case, the Republic said.
"As a family, we have decided we have no comment," Murphy said in a statement Thursday.
CPS officials declined to say whether any children have been removed from Murphy's home.