Thanks!  That doesn't say anything about the CTC being half for MFS.

It reads as follows:

9. The following credits and deductions are
reduced at income levels half of those for
a joint return:
a. The child tax credit and the credit for
other dependents

See the instructions for 8812, in particular the Line 5 Wks on page 4:

https://www.irs.gov/pub/irs-pdf/i1040s8.pdf

Line 8 of the worksheet shows the income levels at which the CTC begins to be reduced.  For MFJ that's $150K, for MFS that's $75K.  The CTC is reduced at income levels half of those for a joint return.  The base credit amount of $3,000 / $3,600 is the same, regardless of filing status.

Rick