Nondependent - dependent care only

We are a separated couple with a child filing separate taxes. The TurboTax system is letting us both add our child to our taxes, which I thought only one of us can claim. It has the child listed as my nondependent since I entered the child care expense and my ex-wife is claim the child with head of household and EIC.  Is this correct?  Can we both e-file this way?