If you're talking about the "Ruger rail" which came with the gun, it takes Weaver style rings. If that's the case, you might get by with the "Medium height", but even so, you'll likely have to remove the rear sight Ass'y so the scope will sit down. Then of course, due to the drop of the factory stock, you'll find that it's impossible to achieve a proper cheek weld unless you buy (or devise) some sort of riser pad.
What I'm getting at here is that IMNSHO, that 3X9-40 is simply too big/bulky for the Mini platform. Yeah I know, people do it all the time...but just speaking for myself, the few times that I've used a scoped Mini, I much prefered the much more compact SG scopes. Or you could buy an Omega Rail and use a scout scope. Or learn to use the iron sights...It is after all, a knock-around carbine, not a bench rest gun.
Hope this helped, and good luck in your endeavors.
DGW