My child files his own tax return for 2009 since he had income over the threshold. I am not going to claim him as my dependent so he can have a higher standard deduction amount on his return. In this case, can I not get a child tax credit either?

What is the age of the child?
If he is under 19, you can claim him if
He lived with you and did not provide more than half of his support. Your U.S. Tax Return: Requirements for claiming a dependent (http://taxipay.blogspot.com/2008/03/requirements-for-claiming-dependent.html)

If you can not claim him dependent, you will not get child tax credit.