State tax filing

Individuals who are residents or inhabitants of New Hampshire for any part of the tax year must file if they received more than $2,400 of gross interest and/or dividend income for a single individual or $4,800 of such income for a married couple filing a joint New Hampshire return. Therefore, you do not have to file an NH return even if it is generated in TurboTax if you are not required to file.

When you are ready to e-file your Federal you will get to the filing option screen

1.  Select Change next to your state return. 
2. On the Change filing method screen, select I'm not ready to file and Save

Or,

You can delete your State return by following these instructions.

Note: If you've already paid your TurboTax state fees or registered your free version with your state return attached, you can't delete your state return.

1. Sign in and open a section of your return
2. From the menu, select State and then select Continue on the Let's get your state taxes done right screen
3. On the Status of your state returns screen, select Delete next to your state, then answer Yes

Also, please see the link below on deleting State returns:

Delete State Returns

@baileyn