The Truck Permit Office issues Oversize/Overweight permits. You can contact them directly at (225) 343.2345 or (800) 654.1433 or order through a permitting service, who will charge an additional processing fee.
For permit questions see http://perba.dotd.louisiana.gov/welcome.nsf/ for more details.
Except in the case of a permit service:
A person shall first have to be registered by the Department under § 179.5 (relating to the issuance of registration agreement), to be eligible to apply for or to obtain a permit by telefacsimile or another wire method approved by the Department. Otherwise, the application shall be made in person or by mail, accompanied by a certified check or money order.
For more information see here