One of the often quoted maxims of US politics is that the candidate that wins Ohio wins the nation. Of course, using modern technology, we can look at that a bit closer.
As can be seen, those numbers pretty much add up. They add up not just with the true/false test, but with the amount of the vote, as well. The exceptions are in a few landslide years, when Ohio doesn't always swing quite as wildly as the nation. But on the whole, it is true.
(This also explains the one exception to the rule: 1960, when Nixon won Ohio, but Kennedy won the nation. Nixon's victory in Ohio was small, as was Kennedy's victory overall).
According to the formula that shall not be named, there is quite a bit of correlation, and I bet that Ohio would indeed have a higher correlation than another other state, besides maybe Missouri.