DODGE CITY, Kan. — On Election Days past, voters cast their ballots at the only polling place in this town of 27,000: the sprawling civic center on the north side of Dodge City. But with a construction project expected to start there soon, the county clerk moved the polls this year almost four miles away, past the railroad tracks and beyond the city limits.

That switch, which in some places might be little more than a footnote in a local newspaper, stoked anger and was perceived by some Democrats as a blatant attempt to suppress the vote of Dodge City’s Hispanic majority. On Friday, the American Civil Liberties Union of Kansas filed a federal lawsuit asking a judge to intervene and reopen the civic center for voting.

The swift backlash and widespread attention to Dodge City’s change came in no small part because of restrictive voting laws championed by Kansas’ secretary of state, Kris Kobach, a frequent A.C.L.U. foe who also happens to be the Republican nominee in this year’s extremely close race for governor.

“I feel like workers who are not allowed to leave their job to vote will not be able to,” said Ashley Romero, 18, a Dodge City resident who said she planned to vote for Democrats and who was selling papayas and limes to workers outside a meatpacking plant. Ms. Romero said she feared the new polling place would be too far away for some people, and too much trouble for those who work long hours or might not have heard about the switch. “A lot of the voters that really are going to be affected by this election are not going to be able to vote,” she said.