  Nuclear muon capture on the proton and $^3$He is considered both within and
beyond the Standard Model in terms as general as is possible. Explicit and
precise analytic expressions for all possible observables are given, assuming
only a Dirac neutrino in the limit of vanishing mass. These results allow both
for precision tests of the Standard Model and new physics, as well as for the
assessment of the potential physics reach of experiments designed to measure
specific observables. Using these expressions, stringent constraints can
already be inferred from a recent precision measurement of the statistical
capture rate on $^3$He. Likewise, similar constraints should follow the
completion of a precision measurement in progress of the singlet capture rate
on the proton.
