This is book number 1 in the Last Policeman series.
“The cliched plot of the end of the world gets a new look in The Last Policeman. With an asteroid on its way to Earth, normal life has already shut down. Faced with certain doom, people decide working is a fool's game and head off to fulfill their 'bucket lists,' except for a very few, including Detective Hank Palace. His only desire is to be a policeman, so he can't help trying to solve crimes even though it's a thankless job. Modern technology is useless with no workers to keep it going, so Hank uses old fashioned footwork and reasoned thinking to find a murderer. If certain doom ever becomes reality, I would include this series in my stack of books to read before the end!”
— Ann Carlson, Harborwalk Books, Georgetown, SC