Amelia Flores, a high school senior with plans to become an electrical engineer, eagerly filled out a form to register to vote for the first time at the Kansas State Fair last month. But she left the fair without registering, stymied by a state law championed by Republicans who dominate elected offices in Kansas that requires her to provide proof of citizenship. “I think it’s ridiculous and restrictive,” said Ms. Flores, who later received a notice in the mail informing her that she must produce a birth certificate or other proof of citizenship to complete the registration. “A lot of people are working multiple jobs, so they don’t have time to get this stuff done. Some of them don’t have access to their birth certificate.” Ms. Flores, who said she was born in Washington State, unwittingly joined a list of more than 36,000 people in Kansas who have tried to register to vote since the law went into effect in 2013, but then did not complete their registration. This month, under a rule adopted by the Kansas secretary of state’s office, county election officials throughout the state began to cull names from the voters list, removing people who had been on it at least 90 days. Those removed from the list must start the registration process over in order to vote.