Yes, that is the law.
Projectile must stay in/on your property.
I was shooting the "feral" chickens in my yard with a pellet gun once and the neighbor who was feeding them called the cops.
Long story short, they wrote her up for feeding the feral chickens (unlawful).
I still often shoot in my yard just for practice and in case that mongoose who keeps eating my fruit sticks his head around the corner.
Currently using the Gammo Whisper.
With it's "suppressor" it's not as loud as the other air rifles.
Using the PBA ammo (extra100FPS) it's louder than other air rifles.
If you do go on a compressed air projectile rat eradication program, set up a red flood light at night, get comfy with your "equipment" , acooler and have fun night !
Between baiting, setting and emptying traps, it would take more time than I have to offer.
Around the garden and up at the ranch, we use mint/peppermint oil and plant mint where we want to keep the rats away.
Place plant/oil where rats travel through or to.
Rats HATE mint.
If you nose becomes accustomed to the mint/peppermint oil, time to reapply.
Planting mint is less expensive, lasts longer and you can make Mint Julip's with it, right Tom?