The Naked Sun by Isaac Asimov

When a person is ***ed for the first time on an Outer World called Solaria that has no police force, Earth detective Elijah Baley is called in to investigate. After reaching the planet, he is reunited with his old partner, R. Daneel Olivaw, a perfectly realistic android posing to be a man. Together, they must get down to the bottom of the mystery, only there is one problem: nobody on the planet can stand to be in the presence of each other! This is the second novel in Isaac Asimov's Robot series.