  The sensitivity of rotational transitions in CH and CD to a possible
variation of fundamental constants has been investigated. Largely enhanced
sensitivity coefficients are found for specific transitions which are due to
accidental degeneracies between the different fine-structure manifolds. These
degeneracies occur when the spin-orbit coupling constant is close to four times
the rotational constant. CH and particularly CD match this condition closely.
Unfortunately, an analysis of the transition strengths shows that the same
condition that leads to an enhanced sensitivity suppresses the transition
strength, making these transitions too weak to be of relevance for testing the
variation of fundamental constants over cosmological time scales. We propose a
test in CH based on the comparison between the rotational transitions between
the e and f components of the Omega'=1/2,J=1/2 and Omega'=3/2,J=3/2 levels at
532 and 536 GHz and other rotational or Lambda-doublet transitions in CH
involving the same absorbing ground levels. Such a test, to be performed by
radioastronomy of highly redshifted objects, is robust against systematic
effects.
