She is violating a court order. I'm unaware of her state or Congress passing some law that she violated?
The Supreme Court's decision in Obergefell
requires the States to issue marriage licenses to same-sex couples. Once the decision was handed down, this is the law of the land, whether you agree with it or not. By failing to issue licenses to gay couples, she is disobeying the law. By failing to issue licenses to any couples, she is also disobeying the law, which doesn't give her much latitude to decide whether or not to issue the license.
With that said, I think that Kim Davis was right to sue the State to request that her beliefs - such as they are - be accommodated by removing her name from the certificates. This could actually be a sensible accommodation, but she's not free to not issue licenses in the meantime.
She is refusing to do her job and violating State and Federal law in the process. She's been sued, and when faced with an explicit order to let the people in her office do their job, she told a Federal Judge that she would not allow this. If nothing else, she's in violation of
18 USC 401, as I've previously mentioned in this and another thread:
A court of the United States shall have power to punish by fine or imprisonment, or both, at its discretion, such contempt of its authority, and none other, as—
(1) Misbehavior of any person in its presence or so near thereto as to obstruct the administration of justice;
(2) Misbehavior of any of its officers in their official transactions;
(3) Disobedience or resistance to its lawful writ, process, order, rule, decree, or command.
Wait... let me guess... you're going to say that this isn't a law either?
