State tax filing

It depends.  Please note the following from the Connecticut Tax Forms booklet for tax year 2017 regarding filing statuses:  

"When both spouses are nonresidents of Connecticut but only one has income derived from or connected with sources within Connecticut, only that spouse is required to file a Connecticut income tax return. The filing spouse’s Connecticut income tax filing status is married filing separately, unless you both elect to file a joint Connecticut income tax return. If an election is made, married filing jointly is your Connecticut income tax filing status." (Bolding part of article, italics added)

Since you are not CT residents, your husband's MA income is not taxed in CT.  (Your CT income is taxed in MA, however, which I will address in this answer).  However, if you choose to use married filing jointly as your CT status, your husband's MA income is factored in to determine your CT nonresident tax.  Your CT return would be prepared as if all of your joint income were taxable, and then the amount of tax is prorated to the amount of income you alone earned in CT.  

You may opt to file Married Filing Separate for CT, but you would probably need desktop software for this, as this FAQ points out:   https://ttlc.intuit.com/replies/3301995

However, it probably doesn't make a difference as far as your bottom line is concerned on how you file.  The reason is that Massachusetts will give you a credit for the amount of tax you must pay CT on your income earned in CT (since MA taxes all of your income as your resident state), and CT's income tax rate is lower than MA's, so you should get the same "bottom line" result no matter how you prepare the returns.