Do chain wear indicator tools, such as the Park CC-3.2, work with both 1/8" and 3/32" chains? Or are they chain-specific?

Thanks in advance.

1/8 and 3/32 have the same half inch pitch, only the width is different so a chain checker will work with either.

I have found that chain checkers work equally poorly (generally overestimating chain wear) on either size of chain. Get yourself a good steel rule and use that to measure your chain.