Probably not. Louisiana does not follow the so-called “convenience of the employer” rule, meaning Louisiana companies should only withheld tax on employers working within Louisiana, and not on employees working in another state out of convenience.
Louisiana says, “Employers located in Louisiana—income tax must be withheld on all employee wages earned in Louisiana regardless of whether the employee is a resident or not.”
Check with your employer to be sure.
On what income are employers required to withhold income tax?