NY and CT do not have a reciprocal agreement. (Neither NY nor CT has any reciprocal agreements with any other states.)
I'm not sure what the meaning is of "NY Work" in your question. Are you saying that you will be working in CT about one day a week, and on the other days you will be working in NY? If that's the case, you run into the "convenience" rule, which means that it matters why you are working in NY.
The income you earn when you work in CT is clearly CT source income. The income you earn when you work in NY is clearly NY source income. However, depending on the reason you are working in NY, CT might also consider it CT source income. If the nature of the work requires it to be done in NY, then it is not CT source income. For example, if you are supporting or selling to customers in NY, or running a NY store or office, then you are in NY for the convenience of your employer, and your earnings for working in NY are not CT source income, even though you are working for a company that has its headquarters in CT. But if you are working in NY, and telecommuting to the CT office, because you want to avoid commuting, or prefer to work from your home, that is for your own convenience. In that case, CT will consider all of your earnings to be CT source income. They will treat it the same as if you were actually working in CT. But NY will still treat it as NY source income, because you are actually working in NY. That is where you end up being double taxed.
If you are working from home because of the Covid-19 pandemic, that could possibly change the convenience equation. However, as far as I know, neither NY nor CT has issued any special rules for that situation. (Some other states have.) So you would still be in a double-tax situation.
