If you are collecting Social Security benefits, either SSI or SSDI, then you cannot collect state unemployment benefits at the same time, regardless of the state in which you live. You are considered "totally disabled from substantial gainful employment" by the federal government if you are receiving Social Security disability benefits. If you apply for unemployment benefits you are swearing that you are "ready, willing and able to work". These statements are contradictory and collecting both benefits could get you into an overpayment situation with either Social Security or the state. Either way, you do not want to get stuck with a large bill you cannot pay back.
As an attorney practicing Social Security Disability in the State of Michigan, I can say that the per se rule is that you cannot collect unemployment benefits as well as Social Security Disability benefits. As the last answerer wrote, to do so would be contradictory. To receive disability from the federal government, you must attest that you are unable to do any jobs in the regional economy. To receive unemployment from the State, you must attest that you are ready, willing and able to work. However, I would never advise someone who is collecting unemployment not to apply for Social Security. Just be prepared to be told that you cannot collect both benefits concurrently.
The other answers may be correct with respect to Social Security Disability benefits, but not so if you are asking about Social Security Retirement benefits.
For retirement benefits, some states have an offset against unemployment for amounts you receive in social security benefits. Under current MIchigan law, you can collect both without offset or penalty.
Go to this link to access the State of Michigan publication on collecting unemployment benefits:
Assuming that you are asking about Social Security retirement payments (instead of Disability payments), Michigan will not reduce the amount of your unemployment benefits as long as you meet the other eligibility requirements. See page 6 of the State of Michigan publication for an explanation of how retirement benefits impact unemployment claims.
I do not practice in Michigan so I can not comment on how they handle unemployment benefits but with regard to SSDI the Chief Judge for Social Security has sent a memorandum to all ALJs reminding them that you can not be denied solely because you collected unemployment benefits.
Anyone who practices in social security knows that work as defined by the SSA is not the same as ready, willing, and able. Social Security takes into account, medical impairment, age, education, and experience while unemployment does not. The bottom line is that on numerous occasions I have been successful in having the judge order SSDI benefits even though the person collected unemployment.
Actual legal advice can only be provided by an attorney licensed in your jurisdiction, with experience in the area of law regarding your question. The information provided is for informational purposes only and is not legal advice.