So my roommate, her kids, myself, my mother (who is visiting lt) and my dog live in a duplex and we each pay rent, separatly, to the landlord. The utilities are all in my name except the wifi; that's in her name and I don't have any access to. Since February she stopped paying. Every month I send her a copy of the bill and the breakdown of her half. Every month. She tells me she can't pay or she'll pay it soon, or ignore me. Do I have a case? Can I take her to court?
Roommate isnt paying her half of the utilities, can I sue her?
Yes. The easiest, most economic option is to file a complaint in Small Claims Court, since the amount in dispute most likely is within the limit in the NY jurisdiction even if yours is a town/village court.
Other than that, be sure to read my answer on a very similar matter. There you will find remarks that will help you preempt or defeat the roommates' possible allegations.