It may be very difficult to determine this. Annulment requires a legal (court) case. The records from cases from the 60s--from 50 years ago--may no longer exist or if the exist, may not be findable: they could have been lost or destroyed. Even if they exist and are filed somewhere locatable, in some old government records room or vault, generally, to find the records from the case, which will include the date you seek, you need to know the county the case was brought in, the year the case was filed, and its docket (official case ID) number. If you know those things, you can contact the county court clerk's office and see how you would search for such old records, but without all that information, it is vanishingly unlikely that you could even locate the records.