Yes, according to the Alabama Dept of Revenue instructions, (linked to below on page 4 below under Filing Requirements).
From the Instructions:
Individuals who are domiciled in (or residents
of) Alabama are subject to tax on their entire income
whether earned within or without Alabama. This is
true regardless of their physical presence within Alabama
at any time during the taxable year. Domicile is where
one lives, has a permanent home, and has the intention
of returning when absent. Domicile may be by birth,
choice, or operation of law. Each person has one and
only one domicile which, once established, continues
until a new one is established coupled with the abandonment
of the old.
https://revenue.alabama.gov/incometax/2016_forms/16f40bk.pdf
