If you were taken to a Police station there is a record. Charges drop does not do away with it.
Pops 1 You said it.
From LSP FAQ
Q. I was arrested but the charges were dropped, do I still need an arrest disposition?
A. Yes, all arrest or summons must be listed on your application. Furthermore, you must provide a certified true copy of the court minutes, which reflects the final disposition of the charge and submit it with your application.
(LAC 55:I:1307.7 & 8)