Ian, per Louisiana DFW:
The season for crows shall be Sept. 1-Jan.1 with no limit; however crows, blackbirds, cowbirds and grackles may be taken year round during legal shooting hours if they are depredating or about to depredate upon ornamentals or shade trees, agricultural crops, livestock, wildlife, or when concentrated in such numbers as to cause a health hazard. Louisiana has determined that the birds listed above are crop depredators an that crows have been implicated in the spread of the West Nile virus in humans.