can a parent claim the child and dependent care credit for a 16 year old child who was placed in a rehab facility for part of the year?

Thanks. You make a good point, but I think there may be more to it. First, the code section says a child under 13 or a person who cannot physically or mentally take care of his or herself. Second, she cannot take care of herself alone because of drug addiction and she is not safe at home in that she frequently runs away.  So, the costs include meals and medical treatment & education but also provide  secure environment for her safety, daily routines with respect to physical care, etc.  I may be wrong but I think that part of the cost represents care for someone who can't take care of themselves. I don't know if there are any case precedents or IRS Rulings.

I think this person wanted to trigger the part here: "or a person who cannot physically or mentally take care of his or herself."

The Child and Dependent Care Credit is for Care; Treatment is Medical.

"You may be able to claim the child and dependent care credit if you paid expenses for the care of a qualifying individual to enable you (and your spouse, if filing a joint return) to work or actively look for work."

Read what the IRS has to state:

https://www.irs.gov/taxtopics/tc602