Member of a CT LLC, Live and work in AL and all my income is made in AL. Do I need to file a CT state income tax?

I will provide some comments related to your overall question:

• In general, an LLC that is organized in a particular state is required to file a partnership return in that state.  This assumes that the state in fact has a partnership return filing requirement, as some may not.  CT does in fact have a partnership return filing requirement.
• The CT-1065 will also include a Schedule CT K-1 for each member.  This CT K-1 will reflect the total income or loss and then the income or loss apportioned to CT.
• You will need to determine if you, as well as any other nonresident members, were included in a composite tax return that was filed on behalf of all nonresidents.  There is a box in the upper left hand side of the CT K-1 that will be marked if this is the case.  If a composite return was filed on behalf of nonresidents, then you do not have any further CT filing requirement.
• If nonresidents were not included in a composite return, then you will need to file a CT nonresident tax return and report your share of the CT apportioned income / loss reflected on your CT K-1.
• CT legislature passed a bill effective for 2018 as a result of the federal TCJA which caps the deduction for state, local and property taxes at $10,000.  The bill introduced a new entity level tax on pass-through entities.  
• Your share of the entity level tax will be reflected in Part III of your CT K-1 and will be used when filing your CT nonresident individual tax return.

There is a lot going on here, and especially for 2018, as a result of the new CT legislation effective for 2018.  Depending on the $$ involved, you may want to consult with a tax professional for some guidance.