Often, your separation agreement or divorce decree may speak to who can claim the children, which is something to consider. The IRS primarily cares about who the custodial parent is, which is the parent the child stayed with the most nights during the year.
Presuming all else qualifies, the custodial parent (sounds like the mother) can take the dependency deduction. However, she can give you the right to take them (or 1 of them) using Form 8832.
The software asks all of the relevant questions to determine if you qualify. You can both add them as dependents to assure you qualify and see how it works out best. Keep in mind that other credits are based on claiming the person/child as a dependent (earned income credit, educational credits, child tax credit).
For more on Form 8332: CLICK HERE
For more on qualifying as a dependent: CLICK
HERE
