The clerk/court can catch up and fix the error however it is unusual. This was a mistake and you got the benefit so be careful. And hire an attorney to represent you as that makes it even easier.
I am a criminal defense attorney practicing in Nassau, Suffolk and New York City. The above information is not a substitution for a meeting whereas all potential legal issues can be discussed.
Since the refusal hearing is civil and the DWI (along with the citation for refusing) is criminal, the fact that no refusal occurred (for whatever reason) will NOT help in the defense of your criminal matter.
Depending on how much time has passed since the alleged incident took place, the police may be able to file a request with the DMV for a refusal hearing, but probably will not.
Best of luck!
Refusal hearings, or lack thereof, will not have any bearing on the criminal case (but for if there was a refusal it “may” be admitted in the criminal case as evidence to establish culpability). If it has been so long, you certainly already have an attorney. You should be discussing these matters with him/her. If you don’t have an attorney get one ASAP.