Do I pay inheirance tax on money my dad left me

No - California does not have an inheritance tax, and their estate tax was phased out in 2005. So no tax is due to California. As for federal estate tax, there's an exemption on the first $2M value of the estate, so unless your father's estate was valued at more than $2M you have nothing to worry about. And if it was worth more than $2M, the executor of your father's estate is responsible for determining whether taxes are due, and he would pay them out of the estate's assets. So whatever you receive is tax-free.