The U.S. Senate adjourned last week and wasn't expected to resume until Wednesday; it's unclear why Crapo had remained in Washington, D.C., ahead of the Christmas holiday.
According to the police report, he was alone in his car. It wasn't immediately clear where he'd been or where he was going when he was stopped.
Crapo was a Mormon bishop at 31 and has showed no public signs of a break from his church's teachings.
Church members must follow its guidance — including its rules on alcohol — to participate fully in the faith's rituals, including temple activities that are central to the religion.
Phone calls Monday to Mormon headquarters in Salt Lake City were not returned.
Crapo, first elected in 1998, is expected to take over the top Republican spot next year on the Senate Banking Committee. He also serves on the Senate's budget and finance panels and was a member of the so-called "Gang of Six" senators who worked in 2011 toward a deficit-reduction deal that was never adopted by Congress.
The 2010 bill he sponsored on cutting taxes for brewers ultimately stalled.