Alot depends on which state you are filing for unemployment benefits. On the State of Texas Workforce Commission website where I currently request payment for unemployment claims on a bi-weekly basis, I am repeatedly required to answer "yes" or "no" to whether I was self-employed during that time period. I always select "no". However, I am certain that if I were to select "yes" to that question, then I would be required to report any pre-tax earnings from self-employment for that period. I am not self-employed, I am laid off but my employer recalls us from time to time for a few hours here and there. When I work I have to report my pre-tax earnings for the reporting period. Self-employment would ultimately effect the amount you would get paid by the state. Furthermore, in order to be eligible for unemployment benefits you have to have worked for several or more quarters and paid into the system through your previous employers and/or paid by yourself (self employed). If you didn't work enough or didn't pay into it then you won't qualify for benefits. You should contact your local Unemployment Office, they will answer any questions you may have and should assist you with filing if you are eligible.
Also benefits from unemployment are generally paid without taxes being deducted, so you will need to keep this in mind come tax time in April as it is reportable income. However, in Texas we are given the option to complete a form requesting they deduct tax from our payments but the amount deducted is a set amount for everyone. If you are exempt from tax or get a full refund each year and expect to be exempt and get a full refund this year then I wouldn't have tax deducted.
Whatever you do, do not falsify or lie on any of the questions or amounts reported. If caught, you could lose your benefits and be required to payback what you were not entitled to and/or overpaid. The state can/will garnish any future wages you earn from any future employment in an attempt to recoupe any overpayments or ineligible payments until your debt is paid off. I know someone very closely or was fired and received $3K in payments before the employer argued the case and won. She was forced to repay the entire $3K so I know for a fact they can do it.