A massive search was stretching into its second day for a man who authorities say posed as a police officer and fatally shot a Democratic state lawmaker in her suburban Minneapolis home, an act Gov. Tim Walz called “a politically motivated assassination.

Minnesota state Rep. Melissa Hortman and her husband, Mark, were killed, and State Sen. John Hoffman and his wife, Yvette, were wounded in a shooting in the Minneapolis suburbs the morning of June 14...