If taxes are already withheld from lottery winnings would I be able to claim that on my tax return and obtain money. The winning was in New York. What form should I file.

The ticket was $10,000 and $3,382 was withheld in taxes from the winnings. I was told everyone has until the 31st to send out their forms in regards to taxes because I only have a receipt from cashing the ticket.

I don't recall any other ticket winnings or losses.

Would I actually have to end up owing taxes even if they already took taxes out?