The Sheriff is the Chief Law Enforcement Officer in the Parish . I sent mine to him with a cover letter stating that I was complying with Federal law and no action was needed on his part .
A little story of applying for my c&r in 2005...
I live in the city limits so I sent the copy to the Police Chief's office. I got it back in the mail with a note saying it needed to go to the Sherriff's office. I then mailed it to the Sherriff's office and got it back with a note saying it needed to go to the Police Chief's office. I called the ATF (terrified I wouldn't get the license) and told them the situation. The agent I spoke to asked if I still had the copy and the notes from both offices. I answered yes. Her response was "Well, keep them around; in a file if you have a filing cabinet. You've done what you were supposed to do." Two weeks later my C&R arrived.