Legal Question in Criminal Law in New York

Usually (but not always) when this term is used it means "on a particular date" or within a day or two near the particular date. This could even go up to a week in meaning, but not generally beyond that. It is nonspecific for the reason that, you guessed it, they don't want to be specific because they don't have an actual time or they are covering all bases. Covering all bases is a regular thing in legal practice. I hope this helps.