possibly dumb question about place of birth

I don't even think this is the right sub to post this in, but whatever.

So here's my situation. I was born at the kingwood medical center back in 1999. I'm sure most of you know that kingwood was annexed by Houston in 96. My issue, is that I don't know what I should be putting as my city of birth when it comes to official documentation. Not all of kingwood is apart of Harris County. The hospital I was born at (and my birth abstract) just say Montgomery County. So should I be putting it as Houston or as kingwood when it asks for city of birth?