I received 45,000 from a trust that was administered in the state of Michigan. Taxes were taken out of the trust before monies were distributed. Will I still have to pay inheritance tax in California for the remaining $45,00 I received?

No, Estate taxes are paid by the estate not the heir.

There is no federal inheritance tax. CA also does not tax inheritances.
Read: Your U.S. Tax Return: Tax on Inheritances