This year on mt stae taxes I claimed my ren,but the last few years I did not claim my rent so can I refile back years taxes and claim the rent for them years?

In general most states allow you to file an amended return to claim a refund only up to 3 years after the filing date. So perhaps you could go back to tax year 2006 if you file an amended return by April 15. Check with the state of MI income tax web site to see for sure.