If you're honest, yes. Any income you make will be deducted from your unemployment. Basically, if you get a job that pays more than what you get for unemployment, guess what? You're back to work and the benefits stop. You can't have your cake and eat it too. My wife is a CO3 ( the person who approves or denies you unemployment benefits in N.H) what was your name again?
I graduated a while back and had the same kind of situation when I began working as a contracted data admin. If you work over a certain amount your benefits may be stopped completely. As a contractor you would be possibly better to declare yourself self employed as a company and issue yourself an income from your business (as contract work is generally either short term or seasonal and this would mean your income was regulated to every month) if you earn under a particular amount and work for less than (I think) 16 hours then you might still be eligible for income support and council/housing benefits. Call and ask - Google self employment and you will find the helpline number, would post it but can't remember it off the top of my head and am too lazy to Google myself.