Crime dramas that I think may appeal to a family audience are:

Pushing daisies- A pie-maker, with the power to bring dead people back to life, solves murder mysteries with his alive-again childhood sweetheart, a cynical private investigator, and a lovesick waitress.

Veronica mars- After her best friend is murdered and her father is removed as county sheriff, Veronica Mars dedicates her life to cracking the toughest mysteries in the affluent town of Neptune.