The Patchwork Girl

Blurb

The Patchwork Girl is a science fiction novel by American writer Larry Niven. Part of his Known Space series, it is the fourth of five Gil Hamilton detective stories and the first to be published as a stand-alone novel in 1980. It was later included in the Gil Hamilton anthology Flatlander.
In a break from his usual ARM duties, Hamilton is an acting U.N. Delegate on the moon, attending a conference on Lunar Law. The Belt Delegate, Chris Penzler, is shot by a laser in an apparent murder attempt. The shot came from outside of the window of his personal quarters, which looks out onto the lunar surface. The only person known to be outside on the lunar surface at the time of the attempt is Naomi Mitchison, a tourist and old flame of Gil's.
Gil believes Naomi to be innocent of shooting Penzler, but suspects that she may be lying in order to hide an equally serious crime.
"Naomi Mitchison" was the name of a Scottish writer and poet.