HONG KONG — After months of antigovernment protests in Hong Kong, voters on Sunday had a chance to voice their opinion on the city’s future — and they turned out in droves, shattering the city’s records for turnout.

The election on Sunday was for district council members, one of the lowest rungs of Hong Kong’s elected offices. District councils mainly deal with noise complaints, bus stop locations and neighborhood beautification projects. Elections for them are usually quiet affairs focused on community issues.

But in the midst of the increasingly violent protests that have divided the city, the race took on outsize significance. The vote was the first test of whether the protests could transform public anger that has led millions to take to the streets into actual votes, or whether the populace had grown weary of acts of civil disobedience that have snarled transportation and forced the closing of schools and businesses.