In 2001, the Louisiana Uniform Electronic Transactions Act was adopted. The intent of this act was to remove existing barriers to allow businesses to conduct business by electronic means. Under this act, a record, signature, or contract cannot be denied legal effect solely because it is in electronic form or an electronic record was used in its formation. Also, if the law requires a record to be in writing or a signature, an electronic record or signature satisfies the requirement.

Here are the details of the law:

RS 9:2607 Legal recognition of electronic records, electronic signatures, and electronic contracts

  1.  A record or signature may not be denied legal effect or enforceability solely because it is in electronic form.
  2.  A contract may not be denied legal effect or enforceability solely because an electronic record was used in its formation.
  3.  If a law requires a record to be in writing, an electronic record satisfies the law.
  4.  If a law requires a signature, an electronic signature satisfies the law.

Acts 2001, No. 244, §1, eff. July 1, 2001.

http://legis.la.gov/Legis/Law.aspx?p=y&d=107133

I think that any state agency cannot require you to keep paper copies of applications and associated documentation.  But, I am not a lawyer.  If you are looking at going paperless I would suggest that you contact your legal counsel and also your funders.

Here is an article on this subject by CAPLAW: CAPLAW on going paperless

See federal guidelines for going paperless