Louisiana has no substantial laws differing from the National Labor Relations Act or Labor-Management Reporting and Disclosure Act regarding unions in private sector employment.
Right to work
The state does have a right to work law; conditioning employment on union membership or dues payment is prohibited.
Contact
National Labor Relations Board (Region 15)
Regulations
Louisiana Revised Statutes; Title 23: Labor And Worker's Compensation
http://legis.la.gov/Legis/Law.aspx?d=83311
Labor organizations and labor disputes
Louisiana Revised Statutes §23:821 through §23:991
http://legis.la.gov/Legis/Law.aspx?d=83975
Right to work
Louisiana Revised Statues §§ 23:981 through 23:987
http://legis.la.gov/Legis/Law.aspx?d=84029