No. 

The receipt of the inheritance is not a taxable event. If there are assets like stock or real estate in the inheritance, you may have to pay income tax when you dispose of the assets (this usually is only true if you hold on to inherited assets). The sale of inherited assets would result in capital gains and the basis (used a deduction against sales proceeds  for determining gains or losses) on those assets is the fair market value on the date the deceased passed away.