NO, two people cannot get  EIC for one child, not even divorced parents. In the case of parents, living together, only one parent can claim the child for any tax reason.

• But, you are allowed to decide between you, who that will be.A child can be claimed by a noncustodial parent if the custodial parent signs a waiver (Form 8332) which allows the exemption.  The custodial parent would be entitled to certain credits even if the exemption is waived.  

• You would attach the Form 8332 from the mother (custodial parent) if she completes it to allow you to claim the exemption for your child.  Only the noncustodial parent is required to have this form and attach it to the Form 8453, then mail to the IRS after his e-filed return is accepted..  

• Only the mother is entitled to the credits for having a child living with her,  even though she waived her right to claim the exemption. The noncustodial parent can use the Child Tax Credit, but will not be allowed other credits such as the earned income tax credit or child care credit, as example, because your child does not live with you.  They are reserved for the custodial parent.

• Click the screenshot attached for clarity on questions as the noncustodial parent.

• Personal Info tab
• Edit beside the child
• Follow the prompts and the screenshot