Here is a site listing Springfields municipal code:
Here is the link to an ordinance in regards to the discharge of firearms, BB guns and air rifles.
Sec 78-252 which states:
No person shall discharge any firearm or BB gun or air rifle which propels BBs or other metal by compressed air or gas except when done on his own premises or premises controlled by him, in proper and necessary cases.
(Code 1981, § 26-137)
Now there could be other laws that contradict this or further define or refine it. I haven't looked through your city's ordinances.
You should probably look at Sec 78-258 which is in regards to unlawful use of weapons as well.
I would do several searches relating to weapons, firearms, guns etc at that site to see what pops up. Sometimes fishing for information in various city ordinances can be difficult. In Columbia, when I was trying to figure out any laws that inhibit open carry, I found one rule in regards to public parks that prohibits open carry at them within the city limits and I don't recall that one being included in the ordinance detailing unlawful use of weapons but in the ordinaces that pertain to parks or something like that.
Don't take my word for anything though. My advice is to go to the link where you can look up things for yourself and make your best judgement and call your local authorities and talk to them about what you've read for yourself if you find it confusing.
I hope that helps.