Which parent is allowed to claim child exemption on the tax return

You are allowed one tax exemption for each person you can claim as a dependent on your tax return. In order to claim a dependent on your tax return there are five tests you must meet:

Member of Household or Relationship Test
Gross Income Test
Support Test
Joint Return Test
Citizenship Test
A person qualifying as your dependent:

generally may be your child, stepchild, adopted child, grand child, great-grand child, son or daughter in law, father or mother in law, brother or sister in law, parent, brother, sister, grand parent, step-parent, stepbrother or sister, half brother or sister, and, if related by blood, uncle, aunt, niece, or nephew. The above relatives do not have to live with you.
Also, any person, whether or not you are related to them, who is a member of your household for the entire tax year, except for temporary absences;
must receive more than one-half of his or her support from you;
cannot file a joint tax return with his or her spouse, unless the joint tax return is filed solely to obtain a tax refund when neither the child nor the spouse is required to file a tax return; and
must be a U.S. citizen or national, or a resident of the U.S., Canada, or Mexico.
A child who is paying more than one-half of his or her own support may not be claimed as a dependent and you cannot take a tax exemption on your tax return.

To claim dependency tax exemptions for any child on your tax return, the child must have a Social Security or taxpayer identification number. A taxpayer identification number can be obtained by filing Form SS-5 with your local Social Security Administration office. An original birth certificate and one other document certifying the child's identity must be provided. It takes approximately two weeks to receive a Social Security or taxpayer identification number.

Divorce or Separation

The parent who has custody of the child for the greater part of the tax year generally may claim the child as a dependent on his/her tax return, regardless of who provides more financial support. This rule does not apply if:

the custodial parent gives up the tax deduction by signing a written declaration stating that he or she will not claim the child as a dependent on his/her tax return, and the non-custodial parent attaches this statement to his/her tax return;
there is a written agreement executed before 1985 specifying that the non-custodial parent gets the tax deduction on his/her tax return, and that parent provides at least $600 of support; or
a multiple-support agreement is in effect.

Multiple Support Agreements

Family circumstances are often more complex than one taxpayer providing support for a dependent. The law provides for multiple-support agreements. These multiple-support agreements usually exist when a family group collectively supports a relative, oftentimes a parent.

You can claim the dependent as a tax exemption on your tax return if:

you paid more than 10% of the support;
the amount paid by you and others for the dependent's support is more than one half the support;
each contributor could have claimed the tax exemption on his/her tax return, except that each gave less than one half of the support;
each contributor who paid more than 10% agrees that you can take the tax exemption on your tax return.
Each contributor must sign a Multiple Support Agreement, Form 2120. You then attach them to your tax return. A different person can claim the tax exemption on his/her tax return each tax year.

Phase-out

It's important to note that the tax deduction for personal tax exemptions begins to be phased out if AGI exceeds certain thresholds (e.g. $225,750 for 2006 joint tax returns, and $150,500 for 2006 single tax returns). Each tax exemption is reduced by 2% for each $2,500 by which your AGI exceeds the threshold amount until the benefit of all tax exemptions is eliminated