The Outsmarting of Criminals, by Steven Rigolosi

After recovering from breaking her arm in a New York City mugging, Miss Felicity Prim decides to leave her position at a doctor's office and move to a small rural town in Connecticut to start a new career as an outsmarter of criminals.  She plans to start slowly, but is thrown full on into her new career by the discovery of a body in her basement.  All of the major characters seem to have sprung from a previous century, and look a little askance at the current tendency to rely on computers and other modern technologies.  The modern characters are a little put off by her doilies.