Depends upon where you are. If you only have crows in fall and winter thru spring well there you go. I believe your state is a winter crow state only.Fall and winter is your best bet as the crows head north about spring and they do not necessarily wait for spring to be in full swing to start heading north either.
In my area there is no winter crow shooting at all except in spring and many a time the crows have headed north by the time the season kicks in. Years ago we had year 'round crow shooting although you had to be quite hardy to do it in the depth of winter and there was no problem with "waiting for the spring season" to open...now a days the crows have already gone to their summer residences and when the season opens there are no crows...in spring...I am surprised at all this as crows are voracious bird eaters raiding eggs and baby birds left and right given the birds on the endangered species list but here the F&G department doesn't know much about crows I learned time and time again. But they are having problems with them. The black duck once very common is getting rare...one reason is that they nest in thickets quite a ways from water as when the young hatch the mother leads them a few hundred yards through a mass of danger if they even get that far...since introduction of the large weasel -the "Fisher cat"as it is called we have seen significant reductions in rabbits and ducks generally and various already rare birds such as hawks already endangered are now on the verge of extinction in the greater north east. The fisher came to us about 1975...the effect has been devastating but the f&G is afraid to have a year round extermination program of the useless Frankensteins' monster-the Fisher cat.
One reason i think they introduced the fisher cat was because it is very very efficient at killing regular cats who kill about a hundred birds a week mostly the sparrows and finches..who along with fishers have about wiped out the bobwhite quail. Another bird which suffered depredation by the fischer cat is the partridge and the wood**** ...the fisher cat comes from South east Asia I understand-another reason not to introduce non native species. As a nocturnal animal it has been utterly devastating.So keep an eye on your states' fish and game department and don't allow anything like that.