Bill Clinton, famously, never won a majority of the popular vote. Ross Perot won 18.9% in 1992 and 8.4% in 1996. Is there any clear evidence Perot's candidacy allowed Clinton to carry specific states that helped Clinton to win the presidency?
No. The idea that Ross Perot significantly hurt Bush's reelection chances is not backed up by pre-election polling or exit polls. In 1992, Ross Perot left the race in July before rejoining it in October. The polls in between those two dates showed that Clinton had a massive lead (high teens to low twenties). Also, exit polls showed that Perot voters were not significantly more likely to favor Clinton or Bush, and that most Perot voters were moderates (a group that Clinton dominated Bush in). Now, all of these facts have holes in them. The Bush-Clinton polls were a month before the election, they could have tightened significantly (in fact, the difference between Bush and Clinton did tighten per Gallop polls in late October). The exit polls that asked Perot voters to choose between Bush and Clinton had a large number of people that simply opted out of the race. Would they actually do that? Maybe. Polling can only take you so far when it comes to people, especially when you're asking hypothetical questions. Even Clinton's dominance of moderate voters could be questioned. If Clinton maintained the moderate voters that leaned liberal while Bush lost the moderate voters that leaned conservative to Perot, it would explain Clinton's moderate lead. So yeah, no clear evidence of any Anti-Bush effect, and probably enough evidence to dismiss claims of a strong Anti-Bush effect, but a minor one is not a logical leap of faith.
If you're looking for information on specific states, you're going to get more speculation. Exit polling generally isn't broken down by state, and even if it is, you're looking a far smaller sample sizes. You're basically left with making an argument based on speculation. Perhaps the best chance for Perot changing the outcome of a State would be Georgia. It had the closest margin of any state in the 1992 election (0.59% for Clinton) and then switched to Dole in 1996 (1.17%, the closest victory for Dole). Even that is questionable though. In 1992, Perot actually had one of his lowest vote percentages in Georgia (it was his 44th State by voting percentage), and Georgia was still a Dixiecrat state in the Legislature and Governor's Mansion. So yeah, no clear evidence that they'd have voted for Bush if Perot wasn't in the race, but at the same time it is certainly a possibility.
Other Possibilities for '92 State Switches: (I'll admit these may be better than Georgia, but I don't know their state level politics that well)
Montana (Electoral Votes:3): Switched in '96, Large Perot vote (25.7%), Small Margin (2.51%)
Colorado (8): Switched in '96, Large Perot vote (23.0%), Small Margin (4.26%)
Nevada (4): Large Perot vote (26.2%), Small Margin (2.63%), Got closer in '96 (1.02% Margin)
I've focused on the 1992 election because we should see a larger Perot effect then. Also in the 1996 election, the top 11 states for Perot either voted for Dole (Republican) or Clinton had over 50% of the vote.
Sources:
The Man Who Supposedly Cost George H. W. Bush the Presidency by Tim Hibbitts
Speaking solely for the 1992 campaign: a somewhat forgotten fact is that Ross Perot officially dropped out of the race entirely in summer 1992 and reentered several months later. At the time he dropped out he was leading in the polling of the three way race. Once he dropped out and after the democratic national convention is when Clinton took a sizable polling lead on George bush, so much so that the Bush campaign itself viewed Perot re entering the race as a good thing. The race did substantially tighten at that point.
Election polling, especially months ahead of an election should not carry a lot of weight of evidence of anything. Races often times tighten, and polling can not identify the cause. Political spin often tries to attribute shifts in polling to specific events. Conventional wisdom in conservative circles believe that Perot caused Bush to lose the election. There is little evidence to support that claim.
The heart of your question is this: if Ross Perot was not on the ballot on Election Day would either candidate have received a larger share of those votes? There are so many what ifs and assumptions hidden in that question. And that also excludes what impact his presence in the race itself affected voter decision making (I.e. News coverage would have been different, debates different, etc).
I was unable to locate specific data at a state level about Perot voters and who their second choice was. So my overall answer is there is no evidence that indicates Perot caused bush to lose a state he would have otherwise won.
Addendum: the generally held belief in political circles is that bush would have lost re election with or without Perot.