I live full time in VA but own a house in NH. I paid real estate tax do I have to file anything in NH?

[DanielV01]

No, you do not have a NH filing requirement.  New Hampshire does not have an income tax, and it's tax returns are very limited to certain types of investment income, which is not the case here.

Having said that, you may still deduct your real estate tax you pay on the home in New Hampshire.  If it is a rental property, then you will do so on Schedule E, which can be accessed by the information in this FAQ:  https://ttlc.intuit.com/replies/3288530

If it is a second home (like a vacation home, for instance), then you may deduct the interest and real estate tax as part of your itemized deductions.