The lawsuit against a clerk who issued marriage licences to gay and lesbian couples, and refused to stop doing so, despite instructions from the attorney general, has begun.

Hillary Hall, a rogue county clerk in Boulder County, Colorado, has married over 34 same-sex couples – including a state senator – despite the state maintaining a ban on same-sex marriage.

Solicitor general Dan Domenico warned her last month that she could face legal action for issuing licenses.

As she has refused to cease issuing licenses, Republican Attorney General John Suthers filed a motion with Boulder County District Court, aiming to stop the clerk.

Arguments will be held on Wednesday in the case, but a judgement by District Judge Andrew Hartman is unlikely to come on the same day.

Hall argues that the marriages of couples in the state should be recognised, that the state should accept that same-sex marriage will happen there, and that marriages should be able to take place while an appeal takes place.

Her supporters gathered outside the courthouse in Boulder.