Can New Hampshire condo association turn off water for nonpayment of condo fee?

Yes, in a word.

If your water is paid for by the assessments you promised to pay when you purchased your unit, and you do not pay your assessments, then the association can deny you access to services, including water, for which you refuse to pay.

Read your governing documents to more fully understand both your responsibility to pay assessments, and the association's duty to collect them, and the lengths to which the association can go to satisfy your debt.