Since it appears, in this case, that the library is only where council members meet and there are no indications of other town government functions occurring here, we would not collect a city/town hall point for the library.
A point should only be placed on a building where normal city administrative type business is conducted, and since Nassawadox does not have such a place, you do not have to add a city/town hall point in this location.
If you're ever unsure about whether or not a feature exists, and it can't be verified with internet research alone, you are certainly welcome to make a phone call or two if this is something you're comfortable doing. We don't require volunteers to make phone calls, so this is completely optional, but in some cases might be useful.