Can anyone here who owms one or more NFA items tell me if they must be registered with the State Police/Dept of Public safety once they have been approved by the ATF?

They do, I just don't know the process.

Brian

You are required to submit an application to transfer to the state police.  This is a simple one page form, they will mail the approved form to you and you must attach a copy with your Form 4.  Once the ATF approves the transfer, then you must also register with the state police, again a simple one page form that can be processed via mail without any trips to state police headquarters.  Your dealer can provide the state forms or you can get them directly from the state police.  Contact the concealed carry division of the LSP for more information or to request the two forms.

What if its just a SBR on a Form 1?

Don't know, best to check with the state police, but I think you will have to register it with them.  Call the concealed permit division of the state police in Baton Rouge.

Yea the ATF just kicked back my form 1 for not getting the state permit first.