Dogs are property. You've cared for her property. Ask her for the expenses related to caring for the property. After all, she would have paid a kennel $17-$35/day, here in Baltimore.
I will assume that the dog's adoption papers include your name and/or you have a copy of the check used to pay for the dog with your name on it, that the dog is micro-chipped in your name, is under your name with the vet, and is registered with the city in your name.
Tell her she will have to sue you to get the dog back and if she does, you will counter-sue her for your expenses in caring for the dog for the last 8 months - vet bills, food, plus daily board, which averages $20 - 30 per day. Then stop taking her calls, e-mails, or texts. If she does sue you (meaning you actually get served, not just threatened), then you should speak with a local attorney for guidance. The Washington State Bar Association can give you a referral: http://www.wsba.org/
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.
"She left the dog with me, saying that she wasn't allowed to have dogs in her new apartment. Since moving out, she has visited the dog maybe twice, but outside of that, we haven't spoken. She has not paid for any of his food, grooming, or any other care items. She has not cared for the dog in anyway shape or form (I take the dog for walks, outside to go to the bathroom, etc...). "
On the facts as you state them, even if her name is the ONLY name associated with the dog, she has abandoned the animal. As noted in the above answers, even if she actually does file a claim, your defense would be abandonment and you would further be able to assert a COUNTER-claim for all costs you have incurred caring for what she claims to be her animal, including your time for taking care of the dog.
Should she actually press the issue in court, your state and local bar associations can assist you with referrals for qualified counsel.