Let's see...Indiana has had a Republican Gov. now since the 2004 election. Prior to that, we had Dem govs for 16 years. And, until the Dems fled to Illinois a few years back, control of the GA was usually pretty competitive, too. So let's test your claim here with voter turnout data in Marion Co. going back to, say, 1992 (before the Republicans had the political power to order tacks and hot coals to be thrown in front of the doorways to urban polling places):
1992 - 69.8% (incumbent IN Gov, Dem)
1996 - 58.9% (IN Gov, Dem)
2000 - 50% (IN Gov, Dem)
2004 - 54% (IN Gov, Dem)
2008 - 55% (IN Gov, Rep)
2012 - 56% (IN Gov, Rep)
2016 - 53% (In Gov, Rep)
So, ever since the 2004 election (when we elected our first Republican governor in 16 years), turnout in Marion Co. has been pretty consistent. They did have a huge falloff between 1992 - 2000. But the state had Democratic governors then.
If Republicans, since gaining power in the state, have really made it hard for urban voters to vote, it doesn't show up in the turnout data.