In New York, where same-sex marriage is legal:

Rose Marie Belforti, the town clerk for the small town of Ledyard, has publicly stated that she will not sign marriage licenses for same-sex couples and refused to do so for Katie Carmichael and Deirdre DiBiaggio on Aug. 30. [...]

Shortly after New York legalized marriage equality, Carmichael and DiBiaggio began making plans to wed. But Belforti, the publicly elected official responsible for issuing marriage licenses, refused to issue one herself and told the couple to make an appointment with a deputy town clerk. There's just one problem: There is no deputy town clerk.

Belforti has cited religious reasons that prevent her from issuing marriage licenses to same-sex couples.

I agree with Unicorn Booty: Fire her. I mean, sorry if she believes that religion forbids her from marrying gay couples... but marrying people under state law is her job. If my religion forbade me from typing petulant screeds, I can't imagine I'd be employed much longer, either.