Zvezda73,
A good place to start digging into this is
https://www.marylandtaxes.gov/forms/Tax_Publications/Administrative_Releases/Income_and_Estate_Tax_R...
which says:
An individual may also be a resident of
Maryland, even though not domiciled in this State,
if the individual maintains a place of abode in this
State for more than six months of the taxable year
and is physically present for 183 days or more
during the taxable year.
which, as the relocation to CA senior living was in September and the home is still owned and used in Maryland, at least leans towards allowing for joint filing in Maryland. This is also supported by the Maryland income tax booklet https://www.marylandtaxes.gov/forms/current_forms/resident_booklet.pdf instructions:
You are a resident of Maryland if:
a. Your permanent home is or was in Maryland (the law refers to this as your domicile).
OR
b. Your permanent home is outside of Maryland, but you maintained a place of abode (a place to live)
in Maryland for more than six months of the tax year. If this applies to you and you were physically
present in the state for 183 days or more, you must file a full-year resident return.
Looking also at page 4 of that booklet, there is a filing status table which shows details for married filing options.
With respect to California, and assuming the senior living is the person's new permanent or indefinite period of domicile, it would be appropriate to file a 540NR return with that state. It can be filed either jointly or as just one married filing separately for the person in California. See
https://www.ftb.ca.gov/forms/2022/2022-540nr-booklet.html
for more information on the California part year resident return. Note that the state tax imposed by California will lead to a credit against the joint Maryland resident return because the same income is being taxed by both states.
