In Michigan, if I miss the homestead exemption deadline, can I get that tax money back?

I'm buying a house but will close after the May 1st deadline to file for the homestead exemption on my property tax. The house now is not homesteaded so for the first 15 months or so I will have to pay the non-homestead taxes that were paid in 2010. Is there any way to get that money back? Like, can I claim that as tax over payment on my income tax return or something like that?