I believe the answer to your question is "no" since I'm guessing you don't have a copy of the previous iOS and Apple does not make them available for iOS's.
However, I don't think your issues are related to 9.3 exclusively. It may have been a bad install. If you open iTunes and connect your iPad, you will have some installation options. Alas, I can't say what they will be (don't have the setup at the moment), but one should be fairly obvious, something like "Restore" or "Reset". It's worth a try.
I just saw your other post on another topic and you can't run your iPad on your laptop. So back to the Apple Store for another connection and installation??
Edited by Ira L (06/24/16 06:50 AM)
Edit Reason: Read other post
On a Mac since 1984.
Currently: 27" iMacs, Macbook Air, macOS 10.14.x,; iPhones, iPods and iPads galore!