They have probable cause to believe that you considered purchasing a weapon and started the paperwork. They have no proof that you completed the purchase, let alone that you still own the weapon or that it is stored at that address.
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
They do not have real probable cause to believe that a felony has been committed or that a particular place should be searched for a particular thing. Of course, that's only if the 4th Amendment is taken seriously, and that restriction on FedGov is out of date now that America has been fundamentally transformed.
“Of course, that’s only if the 4th Amendment is taken seriously, and that restriction on FedGov is out of date now that America has been fundamentally transformed.”
The 4th amendment? I can think of a whole lotta instances where the 4th is routinely violated. I don’t think for a minute that the cops, judges and courts in Connecticut will let a little ole civil right stand in their way.