I won $5,000 on a lottery ticket. I paid $200 state tax when i cashed in my ticket. On my state tax form it shows $5,000 winnings as income. Was I taxed twice?

On my tax return it carried the $5,000 over to my state but I have already paid $200 state tax up front.  The lottery office gave me a check for $4800 and they said it was to pay the state tax.  On my state tax form it shows $5,000 added in my income.  Was I taxed on that $5,000 again?