I don't know about the "most states" part. I know California does not, and that Arizona does. That often results in taxpayers paying foreign tax once and getting credit for it twice. Enough to make some wealthy investors in foreign companies move to Arizona, although Nevada or Texas is usually their choice.
When you think about it, why should the state allow any credit? Most of the returns I prepare show a full credit for the foreign tax paid, which is under the $300/$600 cap for avoiding Form 1116. Taxpayers get their money back that way. California (and probably other states) doesn't allow a deduction for federal tax. Foreign tax is just another federal tax, just not a US tax.
