Before you revised your post, you mentioned about saying in CT for 4 days and 3 days in Canada. You do realized that after your accumulate 181 days in US in a single year, you are deemed a US CT resident.You will not be able to avoid paying CT taxes.
Please refer to what I said above regarding "information" conveyed with high levels of certainty.
The U.S., like Canada, has residency statuses for many diverse purposes. There is residence status for DMV (e.g., driver's license, car registration, auto insurance); residence status for tax purposes (many jurisdictions also have non-residence status for tax purposes; some cities and counties assess their own income taxes for residents and non-residents); residence status for immigration purposes; residence status for health insurance purposes; and many other purpose-specific residence statuses.
Each state (city and county, where applicable) determines residence and non-residence (where applicable) status for tax purposes. The only way to determine your exact status for your jurisdiction(s) is to: (i) consult with a competent tax accountant certified in the state you will be working; (ii) obtain written opinions from the taxing authorities you may be subject to; or (iii) carefully review the tax code and associated regulations, enforcement advisories, and court rulings/precedents for the jurisdiction in question.
As a general guideline, if you live in the USA more than you live in Canada and/or for at least 181 days a year, you
may be classified as a U.S. resident for tax purposes. This is a Federal (not State) "guideline", not an absolute rule. There are many factors that contribute to a determination of "resident for tax purposes". (For some purposes, a person who accumulates at least 30 days of presence in the U.S. in a tax year is considered a tax resident for those specific purposes.) At any rate, employee (W2) earned income in, or sourced in, the U.S. is generally subject to U.S. tax withholding and would generally make the employee a "U.S. Person for Tax Purposes".
Maintaining your Canada residence as your
primary residence and place of domicile (which speaks mostly to immigration status and eligibility to apply for citizenship) is separate from being classified by the I.R.S. (U.S. equivalent of the C.R.A.) as a U.S. Person for Tax Purposes or by a state/county/city as a [non-]resident for tax purposes. (For example, I am a "tax resident" in two countries, two U.S. states, and two Canadian provinces; I am a "taxable non-resident" in three other countries. My tax status as "resident" or "non-resident" has no impact on my "immigration" status in any country.)
This is, in my opinion, examples of some people trying to scam the system to get Citizenship is the shortest amount possible while working/living outside Canada. And you wondered why the conservatives brought in "intend to reside" clause for the citizenship process.
My, aren't we holier than thou this morning. Nothing that has been discussed in this topic even remotely resembles a scam or fraud. These are all very legitimate questions pursuing a very legal course of action. I have found the cross border experience of living primarily in one country while working primarily in another richly rewarding on many levels.