It is my understanding that New Hampshire has opened adoption record information but, to what extent and who do I contact for these records?

I am looking for the adoption information of my great grandmother. She went by the name of: Katherine Lillian Piper. Her parents are listed as James William Piper and Melissa Lillian Sawyer. I can not find a birth record or death record for her. I have only her marriage record. She married in Plymouth, Grafton, New Hampshire in 1901. At that time she was 19 years old which would make her born about 1882. Her marriage record states she was born in Woodstock, New Hampshire to James William Piper and Melissa Lillian Sawyer but I have found the death notice of James William Piper and it states Kate was his adopted daughter : "He leaves a wife and adopted daughter, Katie"

This leaves me to wonder who her biological parents were and I can not go on with my genelogical research without this information.

If anyone knew this family or knows how I can get the adoption records for Kate, please contact me as this information would be greatly appreciated.
Thanking You In Advance,
Angie