What constitutes a close enough connection to any given state depends on the laws and court rulings of the state that wishes to impose a tax on a trust.
Nevertheless, with states often facing revenue shortfalls, it is no surprise that legislatures are continuously passing laws in an attempt to mandate that more and more trusts can be taxed by their states.
Because of these state tax issues, it is very important that you have your trust created by an experienced estate planning attorney who can help you navigate tax issues.
Remember also to revisit your trust with your attorney from time to time as state tax laws do change.
When it comes to any government and taxes, you need to stay involved to minimize the tax burdens on your trust.