No, two people cannot take a dependent exemption for the same child.  However, if you are the custodial parent and waive the exemption to the noncustodial parent you will still list your child on your return.

Only the custodial parent is entitled to the special credits below because the child lives with them assuming they are a qualifying child (Qualifying Child Rules attached).

• 1. The exemption for the child. - Option to waive to the noncustodial parent 
• (Completed by the custodial parent Form 8332 must be attached to the return of the noncustodial parent)
• 2. The child tax credit. 
• 3. Head of household filing status. 
• 4. The credit for child and dependent care expenses. 
• 5. The exclusion from income for dependent care benefits. 
• 6. The earned income credit.