The question is of DOMICILE= do you intend for the house you purchased in New York to be your home- the place you go back to after absences? If so, you can establish New York as your domicile and use the above exception so you do not have to file the New York state tax return.
A person can only have one DOMICILE, so if this is the case, because of the number of days you stayed in Connecticut you would still be a Connecticut "tax resident" so you would file as a CT resident.
@kushanperera
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