Trust residency

Florida does not impose a state income tax on either the grantors or the trust.

It depends.  First, since the question is about filing a form 1041 I assume the trust is not a grantor trust and is irrevocable. According to the IRS:  "If a trust is a grantor trust, then the grantor is treated as the owner of the assets, the trust is disregarded as a separate tax entity, and all income is taxed to the grantor."

If the trust is not a grantor trust then it is it's own entity.  So as TagTeam mentions FL does not tax trust income or the grantor's income, if the trust is disregarded for tax purposes.  

Now the question is will CT.  Here is a link for reference.  The  Irrevocable Inter Vivos Trust is an entity of it own.  

"A trust is either a resident trust, nonresident trust, or part-year resident trust. The residence of the fiduciary or the beneficiary does not affect the status of a trust or estate as resident or nonresident.

Fiduciary applies to a person who occupies a position of special confidence toward others, such as a trustee, executor, or administrator. A fiduciary is a person who holds in trust property in which another person has a beneficial interest or who receives and controls the income of another."

If the grantor was a resident of CT when the item(s) were transferred to the trust then the trust is a CT resident Trust.  If that is the case then the trust will file as resident in CT reporting income no matter where it was earned.  

If the Trust is non-resident (grantor was non-resident when item(s) transferred in) then only if the trust has income from CT sources it will file in CT as non-resident and allocate CT source income to CT (see below).  

"Income derived from or connected with sources within Connecticut includes income:

• Attributable to ownership or disposition of real or tangible personal property within Connecticut including but not limited to the income from the rental or sale of the property;
• Gains and losses from the sale or disposition of an interest in an entity that owns, directly or indirectly, real property in Connecticut. See Sale or Disposition of an Interest in an Entity that Owns Property in Connecticut;
• Attributable to compensation for services performed in Connecticut or income from a business, trade, profession, or occupation carried on in Connecticut;
• From a partnership doing business in Connecticut;
• From an S corporation doing business in Connecticut;
• From a trust or estate with income derived from or connected with sources within Connecticut; or
• From reportable Connecticut Lottery winnings. 

A trust or estate carries on a business, trade, profession, or occupation within Connecticut if:

• It maintains or operates desk space, an office, shop, store, warehouse, factory, agency, or other place in Connecticut where its affairs are systematically and regularly carried on; or
• Business activities are conducted in Connecticut with a fair measure of permanency and continuity for livelihood or profit as distinguished from isolated or incidental transactions."