My daughter is trying to establish residency in another state. Does this mean I can't claim her as a dependent?

[Opus 17]

Very likely.   It's a bit complicated, and we would really need to know what your daughter is doing and why, and exactly how.

Assuming your daughter is under age 24 and a full time student, she is your dependent if she lives in your home more than half the year, and does not provide more than half her own support.  Students are generally considered to live with their parents, and time away at school is a temporary absence. This assumes your child would return home for vacations, school breaks, and summer.

If your daughter establishes her own permanent home or domicile away from your home, then she no longer "lives with" you, and can't be claimed as a dependent under that standard.  (There is a second standard under which you could claim her, but only if you pay for more than half her support AND her taxable income is less than $4500 a year.)

A person only has one domicile at a time. Your domicile is your true and permanent home. There is no single factor that determines where your domicile is located, it is a combination of all the facts and circumstances of your life. Key factors include location of your job, your home, your significant friends and social relationships, your doctor, your attorney, your church, your children’s schools, your voter and vehicle registration, and so on. It is where you plan to return whenever temporary assignments are over. In order to establish a new domicile, you must also take active steps to abandon your previous domicile.

So the question is, whether your daughter has abandoned your home as domicile and established a new domicile somewhere else, and what date that happened. 

Remember that you can still claim your child as a dependent if she lived in your home more than half the year.  As long as she did not establish her new domicile until on or after July 2, then she still lived at home more than half of 2023 and can be claimed as a dependent.  (She would not be a dependent for 2024.)  Also, you and your daughter need to know that she must answer "Yes, I can be claimed as a dependent" if she can be claimed, even if she does not want to be claimed for that year. 

I would also inquire briefly into her financial resources.  If she is paying more than half her own support costs (totaled over the whole year), that also disqualifies you from claiming her as a dependent.  Food, rent, clothing, travel, tuition, medical, etc.  Note that if she pays for tuition with loans taken out in her name, that counts as support she is paying for herself.  (Scholarships do not count as support.)

[Hal_Al]

I agree, with @Opus 17, it's very likely that she can no longer be your dependent, mainly because she is considered as no longer living with you. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.  Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit.  Either gets the parent the $500 Other dependent Credit. 

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4400 (2022).
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer

[Critter-3]

Ask the college financial office for further information ... trying to artifically setting up residency in another state solely to get lower  in-state tuition  is not that easy ... many schools have rules on how it must be done to qualify.