If both of you claim the the IRS uses tie-breaker tests.
The child will be the qualifying child of:
1st -The parent,
2nd- the parent with whom the child lived for the longest time during the year,
3rd- If the time was equal, the parent with the highest adjusted gross income, and
4th, if no taxpayer is the child's parent, the taxpayer with the highest adjusted gross income.
A child can only be a dependent of one person (only one person can claim successfully)
HOWEVER ... if she didn't work that much the exemptions may not do much good. The filing threshhold for 2012 for a single filer is 9500.
See this: http://www.efile.com/tax/do-i-need-to-file-a-tax-return/
Also if she did work a little, had tax withheld, and is trying to get a refund, its most likely that YOU taking the exemptions will bring back more money into that house.
Again one exemption takes 3800 off of your taxable income
SO if you're in the 25% bracket and she's in the 10%, thats 3800x4 off of your incomes ... $15,200.
At a 25% tax bracket, the tax benefit brings 3,800 back into the house. At a 10% tax bracket (income less than 17,400) that only brings 1,520 back into the house.
Maybe if you can help her understand that (or maybe even, worst case, offer her some of it, or offer to buy groceries with it) she will do the smart thing.
But if you both claim them, she would win the tie-breaker.
I know this might not be good news, but it's accurate.
(I hope you'll rate my answer on its accuracy and thoroughness, rather than any good news/bad news content. PLUS knowing the facts, may help you to "see around some corners.")