The child can only be claimed by one parent. If your former girlfriend claimed the Child Tax Credit (CTC) and your daughter as a dependent (a requirement for the child tax credit), then for you to claim daughter/CTC you will need to complete your tax return and mail a paper return (you won't be able to efile).
Then the IRS will become involved and send letters to you both to sort out who the dependent/CTC belongs to. Be certain to document that you are eligible to claim your child as a dependent and the CTC, and answer the IRS letter.
See the links below to check your eligibility for both.
Who can I claim as my dependent?
Do I qualify for the Child Tax Credit?
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