I was arrested in New York on domestic violence charges, how long before it is dismissed?

I suggest you read the case at: http://law.justia.com/cases/new-york/other-courts/2006/2006-52137.html

The complaining victim has to sign the supporting deposition within 90 days of your arraignment pursuant to CPL 30.30. If the C/V does not sign, the DA's office can try to go forward with the case, but it will be extremely hard. The case will most likely be dropped if the C/V does not sign.

Yes, the complainant must sign the supporting deposition. The DA may be able to proceed with out it if there are other witnesses. If the victim is truly not wanting to cooperate then they should go in to meet with the ADA to explain this and perhaps a notarized statement should be procured attesting to that. You should not contact this person under any circumstances, as you are subject to an Order of Protection and could be charged with Criminal Contempt if you do so. Public defenders are usually pretty competent, but in my opinion they have too heavy of a caseload to give meticulous attention to every matter they have. Good luck with everything.

90 days from arraignment on a misdemeanor.

90 days from the first court date.