Winter Widow by Charlene Weir

San Francisco policewoman Susan Donovan moves to Hampstead, Kans., when she marries the small city's police chief, Dan Wren, only to become a widow within six weeks. Shocked and enraged, Susan gets herself appointed Hampstead's temporary police chief and vows to find Dan's killer. When a reporter, daughter of the area's leading family, is strangled while investigating Dan's death, the mayor responds to local pressure and threatens to fire outsider Susan before more citizens die. She wins a five-day reprieve but must survive various assaults, from humans and animals, before she can solve the cases.

I had read a later book in the series and her backstory intrigued me so I finally read the first in the series.  Coming from the midwest you get a real feel of the cold isolation that the open plains are. She has to deal with a small town mentality where men run the show.  Much of the story is her internalizing the situation and trying to deal with the grief she is feeling.  Not bad for a first book.