You can look up relatives if you've hit a dead end. Some private companies provide an address match of the subject you're trying to search, along with a list of possible relatives. You will need to use your judgment when looking around, but, the information free and you can gather helpful information. When looking up records, the full name, including the middle name if available, is going to be an essential part of your investigation. The date of birth is helpful also which you may be able to see for free. As you go, you'll pick up more information to expand your search.
Try an inmate search, if the conviction was a long time ago with a sentence to a state facility, the New Hampshire Department of Corrections (DOC) Inmate Locator has a free search, there may more throughout local departments, such as Belknap county, where they have an online inmate search.
Look up "Support Services Bureau Criminal Records Unit" and you will see information about the criminal report's coverage. The first paragraph mentions that it includes arrests and dispositions of individuals charged with a criminal offense in New Hampshire. Couldn't tell if arrests alone show up or only when they've resulted in a case and convictions, however, the webpage claims that it is the only source for an individual’s complete criminal history for all of New Hampshire. There are fingerprint based searches that can be conducted from the same webpage.
There are a few bits of information that is important in getting arrest reports, such as which police department made the arrest. The more you know about the arrest, the easier it will be to find out about the arrest. Did the arrest result in a conviction where it can be found in court records. Is it a recent arrest where inmate lists from individual police departments would show some details. Is the person currently in the department of correction's custody, you can use the New Hampshire DOC's inmate locator. You won't need a location as the entire state is searched at once. The only information you will need to begin is a partial first and last name.
RSA Chapter 91-A is one place to look it up, here’s a link to a table of contents dealing with access to governmental records and meetings. http://www.gencourt.state.nh.us/rsa/html/vi/91-a/91-a-mrg.htm
You can also get information about the records open to the public directly to the department first. They’re supposed to be along legal guidelines. Each can different laws applying to them. Usually it’s the line between public and private records.
The instructions to request public records on some forms from the individual agency also will offer a good picture of what is required when making the request