Much like the federal government, which has enacted the Uniformed Services Employment and Reemployment Rights Act (USERRA), many states have enacted laws to protect the employment status of the men and women who serve in the armed forces (38 USC 4301 et seq.).
New Hampshire has enacted such a law.
Remember that USERRA, a federal law, preempts any state law that is less protective of the employment and reemployment rights of uniformed service people. That is, if New Hampshire law is less protective than USERRA, then the rights given by USERRA will apply. In addition, if New Hampshire law is more protective than USERRA, then the New Hampshire law will apply.
There is more information.