I think the answer is a a tentative YES, but the correlation can be a little difficult to map and interpret.
First, what do you mean by "political system"? Are you asking if there's a major difference between the ways democracies and authoritarian governments impact human rights and the environment? Or are you focusing on specific regimes, like the U.S. versus Switzerland?
As a very broad generalization, it's interesting that socialism hasn't been much better for the environment than capitalism. The environmental damage in the USSR may have been as bad or worse than the that in the U.S. China is a virtual sewer. (Of course, it was a great civilization in the distant past, meaning people have had centuries to ruin the land.)
Fortunately, some socialist leaders have shown an interest in the environment, notably Bolivia's Evo Morales and Libya's Muammar Gaddafi. The U.S. was a leader in the creation of protected national parks, forests and wildlife refuges.
So it kind of looks (to me, at least) that it's hard to find a clear link between environmental issues and political systems. It might be more productive to look for a link between environmental issues and economic systems. And there are obvious differences between the way specific regimes treat the environment.
Human rights agendas may be even more difficult to measure and correlate than environmental agendas.
It's hard to imagine a country with a better civil rights record than Switzerland. Its citizens appear to be treated pretty fairly, and Switzerland doesn't colonize or wage war against other countries.
Contrast that with the United States, which has a pretty shoddy record on both the domestic and international front. Some would argue that Stalin's bloody purges make the U.S. look like paradise, but the U.S. was built on slavery and a genocidal war against Native Americans, not to mention hostile actions against other countries.
Cuba arguably takes better care of both people and the environment than the U.S. does. The most obvious problem is probably its authoritarian government and relative poverty. But those problems can largely be blamed on the U.S.
In summary, I think a country's record on human rights and the environment reflects a combination of political system, economic system and regime, as well as the literacy and mindset of ordinary citizens. To get a really accurate answer, you'd probably have to list the "political systems" you're referring to, so people could make some comparisons.
I glossed over your request for specific "statistics." I'm going to search for some, but I suspect the answer to that question is NO. This is a topic of special interest to me, and I don't recall ever seeing any credible statistics on this topic.