Ulster County marriage records are locally archived at the town or villages where the marriage license was granted. Thus, it is the first responsibility of the requestors to find out where the marriage took place so they will know which specific office to go to when in need of the said legal documents. In Ulster, county clerks were ordered to make indexes or registers of marriages from 1908 to 1926. Such a practice has been applied up to these days, hence, the locals should be able to pull up the resources which they needed.
At that time, although the documentation stopped in 1926 some of the clerks still continue make summaries of the marriages that transpired within the localities. The details of the record are never divulged in the old days for security purposes, they only were able to provide the requestors with the names of those in the record, license date and the place of issue. Other than that remains confidential as a directive of the local government. Nowadays, the direct office that you should make contact with must be the village, town or city clerk for they for sure have the marriage records Ulster County that you are looking for.