If your K-1 income includes income generated in NY and CT, you must file a non-resident return in each of those states IF the particular state amount you received exceeds that state's filing threshold for non-residents.
You'll find CT's non-resident filing requirements on page 6 of this reference:
https://portal.ct.gov/-/media/DRS/Forms/1-2018/Income/CT-1040NRPY-Online-Booklet_1218.pdf?la=en
You'll find NY's non-resident filing requirements on page 7 of this reference: https://www.tax.ny.gov/pdf/current_forms/it/it203i.pdf
Since you live in CA, ALL your K-1 income is taxable by CA. But if you do have to pay any tax to CT or NY, you'll be able to take a credit for it on your CA return - so you won't be double-taxed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
