How precisely does my place of birth need to match my birth certificate when applying for a US Passport?

I am applying for a US passport as a natural-born US citizen. On my passport application, I listed the city and state I was born in. I was just looking at my birth certificate however, and it lists the county I was born in, rather than the city. Will this cause the Post Office or the State Department to deny my passport?

There are plenty of inhabited parts of the US that are not part of any city or town, so sometimes county is the best you can do.

@DarrelHoffman And there are some incorporated cities (every incorporated city in Virginia, plus St. Louis, Baltimore, and Carson City) that are not part of any county, so sometimes you don't have a county to put there.

@DarrelHoffman Not really. You two are overthinking it: If you live in an unincorporated area and something asks your city, you put down your post office city. what goes in the city spot on your mailing address.

It can also happen that the exact place of birth can be in a different city from where it was at the time of birth, if city borders have changed. As an example, one of my friends lives in what was once unincorporated land in Texas which had "Leander" as the city in their address, and then the boundaries of the neighboring city of Cedar Park expanded so their home was now part of it and their address changed to say "Cedar Park".

@gparyani or the postal routes cross municipal borders and the house is served by the post office of the neighboring town, so the postal address is in a different incorporated municipality from the one where the house is. A childhood friend of mine lived in such a house; his sister still lives there.