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The answer is possibly.
From IRS.gov (https://www.irs.gov/uac/Ten-Things-to-Know-About-the-Child-and-Dependent-Care-Credit):
A qualifying person is your dependent child age 12 or younger when the care was provided. Additionally, your spouse and certain other individuals who are physically or mentally incapable of self-care may also be qualifying persons. You must identify each qualifying person on your tax return.
There are other requirements, such as the care is needed so that one or both adults can work or look for work, etc. The link I provided covers the requirements in more detail.
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"A qualifying person is your dependent child age 12 or younger when the care was provided. " You might have to split the care provided before age 13 and after.
The parent would be entitled to a partial credit for the care provided 1/1 through 4/21/15.