TOPEKA, Kan. (AP) — The leading Democratic candidate for Kansas governor is under attack for her past backing of tough voter identification policies as her party prepares for the possibility that the champion of those measures, conservative Kris Kobach, will win the Republican nomination.

Democrats have regularly criticized Kobach, the Kansas secretary of state, over policies they believe suppress voter turnout. No state had gone further in requiring prospective voters to provide papers documenting their U.S. citizenship when registering, until a federal judge struck down the law in June as a...