If statistics are what they’re really after, using sex from a birth certificate captures the sex of all persons born in the state, regardless of current residency. A census would capture the sex of all current residents in the state, regardless of birth location. Could ask for birth place on the census but that still excludes all persons who were born in and subsequently emigrated from the state.

Chances are high the results between the two would be wildly different. Depending on what they’re trying to measure, either is feasible, just a discussion of which is more appropriate for the intended analysis. As a statistician, I’d personally want both datasets, at the very least for exploratory analysis. I’ll take all the data I can get.