  A largely unconstrained set of relativity-violating effects is studied via
the gravitomagnetic effect on intrinsic spins. The results of existing
comagnetometer experiments are used to place constraints on two new
combinations of these effects at the 10% level. We show that planned
improvements in these experiments will make them competitive with the best
existing sensitivities to this elusive class of relativity-violating effects.
Prospects for measuring the conventional General-Relativistic gravitomagnetic
effect are also considered.
