Yes, you are required to file an LA state return.
Gambling winnings earned in Louisiana is considered to be Louisiana sourced income. A nonresident who received gambling winnings from Louisiana sources and who is required to file a federal income tax return must file a Louisiana return reporting the Louisiana income earned. If the amount withheld is overpaid, a refund of the difference will be issued or credited to the tax liability for the following year, based upon the taxpayer's return.
Source: http://revenue.louisiana.gov/IndividualIncomeTax#nriit