Death Comes to Pemberley by P. D. James has been very popular. The story takes Jane Austen's beloved couple from Pride and Prejudice, Darcy and Elizabeth, and involves them in murder and mayhem. If you haven't gotten your hands on a copy or you already finished it and want more here are a few other titles you may enjoy.
Carrie Bebris has written several books featuring a mystery solving Darcy and Elizabeth. Later in the series some other Austen characters also make appearances, as you might guess from reading some of the clever titles like The Intrigue at Highbury or Matters at Mansfield.
If you would like more of Darcy and Elizabeth and they need not be solving crimes, you are in luck. Typing in Pride and Prejudice in the Title search box in the catalog reveals seventy choices. Some are continuations of the original story and others are cleverly re-imagined scenarios.
If you just enjoy the flavor in Regency mysteries there are some other options. Elizabeth Peters writes the Amelia Peabody series and Anne Perry writes the Thomas and Charlotte Pitt series. Both Amelia and Charlotte refuse to sit quietly at home while there are mysteries to be solved. They may at times even remind you of Elizabeth Bennett.