According to the Oklahoma instruction booklet for individual
income tax returns, a non-resident is
required to file a return if you have gross income of $1000 or more from
Oklahoma sources.
The Louisiana non-resident instructions state that if you
have income from Louisiana sources and
you are required to file a Federal return, then you are required to file a Louisiana
return. You would need to file the
Louisiana return in order to get the refund of the taxes withheld.
See the links below to open the instruction booklets for
more information.
https://www.ok.gov/tax/documents/511Pkt-15.pdf
http://revenue.louisiana.gov/TaxForms/IT540Bi(2015).pdf
