Regarding tax consequences, you really should consult with your accountant, CPA or tax attorney. Either one of those tax professionals are much better qualified than a real estate broker to answer that part of your question accurately.
Property taxes are a function of population, town services and budgets, the percentage of residential properties to commercial properties in each town, to name a few. Connecticut has, traditionally, assessed far lower property taxes than New York...taxation was the driving force behind many corporations leaving the state of New York, in the 80's and 90's, relocating to Connecticut, more specifically. to towns like Greenwich, Stamford and Norwalk. Likewise, residential buyers are attracted to Connecticut because property taxes are lower...but, keep in mind that housing might be more expensive in Connecticut than New York, so you really need to put pencil to paper in order to assess whether the savings in property taxes offsets a potential larger price tag when buying a home in Connecticut as compared to New York.
Regarding other taxes to be aware of in addition to personal property tax: 1) Ct. income tax, 2) Ct. inheritance tax and 3) Ct. estate tax. Again, please consult your tax professional as they are the experts in the area of state taxation and how one state will treat income from another state, as in your case, working in NY but potentially living in CT?