That would depend on why he failed to qualify as a dependent on your federal tax return.
Briefly, the federal rules for claiming dependents fall into two categories:
Qualifying child
- They are related to you;
- They aren't claimed as a
dependent by someone else;
- They are a U.S. citizen,
resident alien, U.S. national, or a Canadian or Mexican resident.
- They aren’t filing a joint
return with their spouse or are filing a joint return only to claim a
refund of withheld income tax or estimated tax paid;
- They are under the age of 19,
or 24 if a full-time student;
- No age limit for permanently
and totally disabled children.
- They live with you for more
than half the year (temporary absences from your home, while living at
school, still count as time living with you); and
- They didn't provide more than
half of their own support for the year.
A new requirement this year is that each qualifying
child dependent must have a Social Security Number, issued before the due date
of your tax return (including extensions) to be claimed for the Child Tax
Credit.
Qualifying relative
- They don't have to be related
to you (despite the name).
- They aren't claimed as a
dependent by someone else.
- They are a U.S. citizen,
resident alien, national, or a Canadian or Mexican resident.
- They aren’t filing a joint
return with their spouse.
- They are related to you or
lived with you the entire year as a member of your household.
- They made less than $4,150 in
2018.
- You provided more than half of
their financial support.
It is entirely possible that your state has slightly different rules, so that a qualifying relative who, for example, failed by making too much income for the federal return might qualify on your state return if the state income standard is different.