This site says it is good. Not excellent. PC is very prone to stress cracking. Molded parts have lots of stress built in to them.

[PDF] Chemical Resistance of Polycarbonate Sheet - palramhort.com

Chemical Resistance Chart and Plastic Material Selection Guide

Molded parts will have to be tested.

Your material supplier is a better source of this type of information.

Talk to your material supplier. We can't give you answers beyond what is on the web.

I say it's not the best choice. Does it have to be transparent?

How to Search the Internet Effectively

SPS Corporation, a greenhouse glazing supplier (first link) lists polycarbonate as resistant to methane at room temperature.

Incidentally, that company's home page comes with a warning from Google. The PDF download wasn't flagged, however.

Miller Plastic Products (second link) recommends that polycarbonate not be exposed to methane.

So if the exposure is going to be long-term, or at other than room temperature, polycarbonate is probably not the best material for this application.

Polycarbonates are resistant to most vapors until they are exposed to UV (sunlight). This combination will accelerate stress cracking.

Don't do it. Use something else.