I double checked with Bill Foreman in Fisheries yesterday when I was in Hartford. After our discussion and thinking about it, Bill sent me the following info. If you are only keeping them as "pets" then it's not an issue. If you are raising them for sale or release then all of the below is applicable:

Yesterday (Monday), you had asked me if one could keep live trout at home in a tank, and whether there were any permits required. I had responded that if they were legally acquired he could keep them at home, with the assumption that the individual wanted to fish for the trout and bring them home.

However, I just read the post on CTfisherman that you referred to and a different picture is emerging. It sounds like he wants to purchase some trout, grow them larger and then sell them. That is a different story. For starters, if he purchases the fish from out of state, he would need an importation permit, and if his intent is to sell the trout, then see CGS 26-114:

Sec. 26-114. Prohibited acts. No species of fish or bait shall be fished for or taken in the inland district except as authorized under the provisions of this chapter and the regulations issued by the commissioner. Any species of fish or bait taken during the closed season for such species, or less than the legal length, or in excess of the daily, season or possession limits for the species involved, shall not be possessed and all such fish or bait shall, without avoidable injury, be immediately returned to the waters from whence taken. No person shall fish, take, attempt to fish or take or assist in fishing or taking or attempting to fish or take any species of fish or bait in the inland district except as authorized under the provisions of this section. Each fish or bait species taken or possessed contrary to the provisions of this section or the regulations issued by the commissioner shall constitute a separate offense. No person shall buy, sell or exchange, offer for sale or exchange, or possess with intent to sell or exchange, any species of trout, any species of salmon specified by the commissioner, black bass, calico bass or crappie, chain pickerel (Esox niger), great northern pike (Esox lucius), or pike perch, wall-eyed pike (Stizostedion vitreum) or any bait species, except as provided under the provisions of this chapter and as authorized under regulations issued by the commissioner. Each fish or bait species sold, purchased, exchanged or possessed contrary to the provisions hereof shall constitute a separate offense.

Additionally, they would need a hatchery license (see CGS 26-149) from DoAG. Much simpler to just keep them as pets. I’ve included Bill Gerrish on this email as he can provide additional insights.

Sorry for misinterpreting the questions,

Bill