Yes to NY. You are a NY resident and NY taxes all of your income no matter where it is earned. If you earn income in another state, you will receive a credit for the income tax you pay on that same income to the other state.
No to PA. Although the company's main office is in PA, your work is not associated with Pennsylvania, but with the Connecticut client. If you were physically going to Connecticut, the income would not be taxable to PA unless you lived there.
No to CT. If you were physically travelling to Connecticut, you would file a nonresident return for Connecticut income. However, telecommuting is not considered by Connecticut as taxable, based on this website: http://www.ct.gov/drs/cwp/view.asp?a=1479&q=277548. It says in part:
Nonresident Employees Working in CT
Wages of a nonresident are subject to Connecticut income tax withholding if the wages are paid for services rendered in Connecticut. Wages of a nonresident are not subject to Connecticut income tax withholding if the wages are paid for services performed entirely outside of Connecticut. (Italics added)
If you were living in Connecticut and telecommuting for a NY office, NY does tax you as a nonresident, but the reverse is not true. You have filed accurately by only filing the NY resident return if you don't physically go to the Connecticut office.
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