Your windshield would be covered in New Hampshire if you have auto insurance coverage on your vehicle in which you could make a claim for the repair or replacement of damage to your front glass. You would need a physical damage coverage such as comprehensive or glass breakage to cover a broken windshield in NH. If you only have minimum coverages of liability then your windshield would not be covered by your own policy.
In most states if you have comprehensive coverage on your vehicle than your vehicle is covered for glass breakage, especially to the front windshield since it is the most important window on the vehicle for the driver to be able to see and operate the vehicle properly.
Some insurance companies, for an extra premium, offer full glass coverage when comprehensive and collision is purchased which covers your car's glass for breakage of safety glass with no deductible.
Some states, such as Florida, have statutes that waive the deductible on your physical damage coverage to have your windshield replaced when there is damage to it. This is in hopes that motorist will take care of their windshield quickly, when there is damage done, so that the driver can see clearly out of the front glass. New Hampshire has no such law to the best of our knowledge.
So if you have physical damage coverage on your vehicle contact your insurance company to make a claim so that you can have your front windshield repaired or replaced if you have damage to it. Your insurance carrier will let you know if a deductible is due or not according to the terms of your policy and New Hampshire state laws.
The NH Insurance Department notes that if your windshield is broken you need to take steps to protect your vehicle from more damage. If you do not take such steps, your insurance company could refuse to pay for any later damage. For example, if you do not cover a broken windshield and rain damages the upholstery, your company could refuse to pay for the damaged upholstery.