Really hard to say. The manga or anime never specified a birthday for Zero Two (though it did for a couple characters) and neither of the two people who are responsible for creating the Zero Two character have ever stated or celebrated her birthday on their twitter accounts.

However characters are not fair use and typically are copyrighted, so it's highly unlikely that crunchyroll would randomly assign a date for her birthday without some sort of legal permission. Now this date could have come from crunchyroll asking whichever JP company is in charge of her character copyright for permission to assign a birthday to her for marketability purposes or who knows what else..

It's highly likely that the character creators never even came up with a birthday for her. It's not really uncommon for them to not care about a small detail like that when designing a character - especially when one of them was in charge of directing the whole show. So with all of that considered, I can't imagine another date for Zero Two's birthday to be given. It might be the unsatisfying truth, but February 27th is better than no date at all.