Snoops, on CBS
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Not to be confused with the 1999 series of the same name.

This ran for just 13 episodes, from 1989-90. It was a dramedy about a married couple, Chance and Micki Dennis (played by real life husband and wife Tim and Daphne Maxwell Reid), who solved crimes together. I don't remember anything more specific than that, except the theme song has always sort of stuck in my head. Of course, I knew Tim Reid from WKRP in Cincinatti, and a couple years before this series, he and Daphne had both been in a show called Frank's Place (Wikipedia), which I must have liked at the time, but which now I barely remember existed. (Though I could probably mix up details of the two shows, in my head.) Anyway, Chance and Micki weren't actually detectives, but... that didn't stop them from snooping into crimes. Or whatever.