Yes, to a point. In this situation as long as you both were living with the children (and they are biological children to both of you), it is acceptable for one parent to claim one child (along with the Child Tax Credit and the Dependent Care Credit) for that child, and the other parent to do the same. However, the parent claiming one child may not claim any of the expenses or credits for the other child they are not claiming.
More information can be found on this website (click on link): Webpage: IRS rules of a Qualifying Child
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"