First of all what crime rate are you referring to? The one reported by that government, the one "felt" by it's citizens (also what part of the citizenry) or the "true crime rate" and how trustworthy are they or how able are you to accurately compute them.
Like a totalitarian country might have a 0% crime rate... simply due to the fact that saying otherwise is a crime. Or it might be very safe for tourists because the government protects it's cash cows from any threats and only presents a favorable perspective of the country, though behind the scenes "threats" can be the existence of regular citizens in their proximity and despite not being counted the government breaking it's own laws to do that is also part of the true crime rate. So the discrepancy between reported, felt by different parts of the citizenry and "true crime rate" (what an omniscient observer would count) can vary drastically.
Also you have different reasons for why people commit crimes, from illnesses and compulsions, to crime being the only or only viable way to achieve the bare necessities, to conditions where you willingly break existing rules without any obvious need to do so.
So if you make something illegal that is an inevitable part of the human condition or the social condition in that country than you're likely going to have a high crime rate, because people can't help doing it anyway regardless of consequences. Or your police apparatus is simply not good at doing it's job.
Which leads to another point that it's not just about the laws but also how they are enforced. Like you could for example make it illegal to breath, so you could imprison (or worse) any and all people at will, but could apply that selectively only to those who you don't like. They would inevitably have committed a crime and the high crime rate among the dissident populations could be used to justify the increased police focus there.
Actually "crime" is anything but an absolute property but something that the government can actively set the rate of themselves. So if there is too much crime they can just declare it not to be a problem, make police look the other way et voilà problem solved, while if there is too little crime (for example to justify a large police apparatus) one could just make something trivial and common illegal and suddenly crime is going through the roof.
Not to mention that penalizing something doesn't have to be a binary between good and pure evil either, like depending on how much you want to suppress a behavior or encourage another behavior you might apply different levels of punishment.
Or with regards to levels of punishment it's not the case that harsher punishments are more effective at deterring crime. Of course no punishment is of low effectiveness as a deterrent and with capital punishment the chance of a relapse into crime is rather low, but even with the existence of capital punishment murder is still a thing, it can even increase in prevalence as you normalize the use of extreme violence as a method of justice. So that killing and dying becomes a part of everyday life and "simply how the world works". Not to mention that harsh penalties can result in people avoiding to report others to the police for fear of unjustified punishment and repercussions by their relatives or criminals might avoid turning themselves in and instead rather fight with the police as they have nothing left to lose.
So it's not a linear effect and might even end up being counter productive.
On the other hand just because it's made easier to do a crime doesn't mean you're actually doing it. Like it's usually always possible to commit murder (getting away with it is a different thing but there's little stopping you in terms of the deed itself), though few people would even consider that. If it were to be legal tomorrow people would probably still not think of it as a good idea as it's something with unforeseeable and irreversible consequences for others but also yourself.
And last but not least there's might be a difference in terms of who makes the law and what options you have to challenge it, so is it a democracy where you could technically take part in the process of actually changing the law if it sucks or is it an autocracy where you have no way to challenge a law other than breaking it and where your dissent only matters if it is shared by a substantial amount of people who are at or near the breaking point?
So the crime rate is not really a good number to compare systems or to rank the degree of freedom within a system. There are or can be correlations of that effect, but there are a lot more variables in play that can easy overshadow that.