I'm certain its Charles Grodin, and there a crime, a murder and/or theft, and Charles Grodin's character passes the investigation's interrogation, including a polygraph test. And it's the big surprise twist at the end that Charles Grodin has a twin and he did it. It seemed like a very low production film.
I think it must have been before he did The Great Muppet Caper, cause it seems to have some light cross over similarities.