John Sides has a good item today on the weak statistical basis for assertions that presidential candidates are helped by same-party governors in swing states. This is one of those chestnuts of American politics that's been asserted forever, and may even for all I know been true once upon a time, but is almost completely unlikely to be true now, or recently.
My biggest question about these claims have always been the mechanism for how it's supposed to happen. Sure, once upon a time, in at least some places, there were big party machines that were labor-intensive and fueled by jobs provided by the public payroll. Ah, the good old days.* Go back to the 19th century, and both parties and elections were very different, so I wouldn't want to make any claims without looking at further evidence. But these days (and John cites an article that finds no effect back through 1932), labor-intensive portions of campaigns are supplied by volunteers easily mobilized by online networking, which can be activated rapidly without needing government jobs as a reward. Other parts of the campaign are nationalized (and have been increasingly for decades now) in ways that render local organizations, to the extent they exist and are tied to in-party control of state government, largely irrelevant. Does anyone think Barack Obama would have raised more money in California in 2008 if a Democrat had been governor there?
The one thing that Reid Wilson mentions that I do think might make some difference would be changes in election law and enforcement. To the extent that Republicans change state laws or practices to make it harder to vote, or conversely to the extent that Democrats in the states where they've had control have made it easier to vote, that may have a real effect. Assuming, that is, that the parties are good at targeting their laws for the intended effects. Even then, however, we're probably just talking about changes at the margins (although Wilson doesn't really claim anything much stronger).
Mostly, though, I don't see any reason to expect it to matter whether a party controls the statehouse or not.
*Note: while I don't advocate a return to classic Tammany-style machines, in large part because the belong with the technology of their time, in general I think there's a very good case to be made for those sorts of parties and the "corruption" that goes with them, ably defended by G. W. Plunkitt in the linked book.