What are the requirements for an ASA girls softball league, non-school, concerning umpire credentials? Do umpires have to be ASA certified regardless of the age levels of the players in a non-school, spring/summer league environment?

Any association of which I am aware require umpires to be certified through that sanctioning body, whether it is NFHS, ASA, USSSA, AFA...etc. This is to call at any level. Besides, you really don't want to call "uncertified" so to speak, as that would mean that you are also uninsured when you are officiating a contest.

And, each sanctioning body's certifications are independent of each other and have no affect or application to the others. That is why we have to go to multiple clinics each year.