  Colladay and Kostelecky have proposed a framework for studying Lorentz and
CPT violation in a natural extension of the Standard Model. Although numerous
bounds exist on the Lorentz and CPT violating parameters in the gauge boson and
fermion sectors, there are no published bounds on the parameters in the Higgs
sector. We determine these bounds. The bounds on the CPT-even asymmetric
coefficients arise from the one-loop contributions to the photon propagator,
those from the CPT-even symmetric coefficients arise from the equivalent
c_{\mu\nu} coefficients in the fermion sector, and those from the CPT-odd
coefficient arise from bounds on the vacuum expectation value of the Z-boson.
