Actually, they can, but only because of the 19th Amendment, which was ratified in 1920. If it were up to the city charter, which was enacted 21 years before that and is still in effect, only men would be allowed to vote in the ironically named hamlet of Sistersville, West Virginia:
SECTION 10. VOTING.
Every male person residing in said City, shall be entitled to vote for all officers elected under this Act, but no person [may vote] who is a minor or of unsound mind, or a pauper, or who is under conviction of treason, felony, or bribery in an election, or who has not been a resident of this State for one year, and of the City of Sistersville for six months, and is a bona fide resident of the ward in which he offers to vote....
That is, all residents of Sistersville could vote, except for minors, lunatics, bums, traitors, felons, and women.
The Wall Street Journal reported Friday that city officials in Sistersville, who apparently haven't looked at the city charter in 94 years, did blow the dust off it this summer in order to find out how to replace the mayor, who had resigned. Turns out that a majority of the city council can fill the vacancy until the next election (that's Section 14), and the city clerk shall perform the duties of the mayor until the vacancy is filled (that's Section 21).
Also, turns out it's technically illegal for women to vote (that's Section 10).
This tidbit was briefly mentioned about halfway through an article in the Tyler Star News about the council meeting in which the mayor was replaced. After the new mayor was appointed, citizens (including Ms. Audist Pancake) complained about their water bills, asked if the former mayor had turned in the keys to city hall (he didn't have any), noted that women aren't allowed to vote, and wondered why all the library's cleaning supplies keep disappearing. That's a mystery that—wait, what was that third thing?
In response to the question about Section 10, the city attorney noted that unconstitutional provisions have no effect anyway, and that revising the charter and recodifying related ordinances would cost thousands of dollars in legal fees and printing costs. For a town of 1,500 people with a small budget, this symbolic move may not be worth the expense. Someone suggested a fundraiser, so maybe this will get done after all, but no decision was reached at the meeting.
Given that the 19th Amendment exists, and that the new mayor, the city attorney, the city recorder, and Audist Pancake are all women, it may be that Sistersville doesn't really need to spend the money to amend the charter. It's not like it is the only town in America with unconstitutional or just unenforceable laws on the books. It would send an important message, but it is also important to have clean libraries. Hard choices have to be made.
Actually, here's an idea. Get some keys made for the library (they don't have keys for that, either), lock it up at night, and then use the money you save on cleaning supplies to amend the charter. Because I'm committed to equal rights, I won't even charge for that idea. Problem solved.