The Last Policeman by Ben H. Winters

In six months, a giant asteroid will hit earth and destroy everything. People have adapted to the news in different ways: quitting work and fulfilling their dreams, committing suicide, consuming drugs, etc. Detective Henry Palace, amid the chaos, decides to keep doing his job. When he's called out to McDonald's because someone has hung himself in the bathroom, Henry feels it's murder, not a suicide. The victim, Peter Zell, was a loner who worked at an insurance company. Henry is slowly able to piece together Peter's life in the last few months, but he faces lots of distractions. His sister is asking him to find her missing husband, his colleagues react to his seriousness with apathy and ribbing, and he's dealing with a lack of intimacy in his life. Set against the crumbling of society, Winters has written a mystery (first in a projected trilogy) with an interesting premise and likable main character. It reminded me of Body Politic by Paul Johnston.