An injured female passenger in the Chevette got out and ran a block to East Avenue before collapsing on the sidewalk, they said. She later told police she was running to get help, officers said.
The passenger's name was not available late Friday.
Outside the church, a trail of blood drops could be seen on the sidewalk leading from the accident scene to East Avenue.
Police said Richard Zarobinski, 43, of the 100 block of North Potomac Street, was charged with running a stop sign, and driving while intoxicated.
No further details were available.
The Chevette was badly damaged. The grill of the car was wedged into a recessed V-shape area at the cornerstone of the imposing stone church.
The church appeared undamaged.
A wedding rehearsal was going on inside Trinity Lutheran when the church was struck, but members of the wedding party heard nothing.
Cheryl Dillard of Hagerstown, sister-in-law of the groom, said the first she knew of the wreck was when she walked outside to look for a missing member of the wedding party, and saw an injured man getting out of the Chevette.
"We were inside in the main part of the church," she said. "We didn't hear anything, not even the ambulance sirens."