  In this talk, I discuss possible bounds on the Lorentz and CPT violating
parameters in the Higgs sector of the so called minimal standard model
extension. The main motivation to this study is coming from the fact that
unlike the parameters in the fermion and gauge sector, there are no published
bounds on the parameters in the Higgs sector. From the one-loop contributions
to the photon propagator the bounds on the CPT-even asymmetric coefficients are
obtained and the c_\mu\nu coefficients in the fermion sector determine the
bound on the CPT-even symmetric coefficients. The CPT-odd coefficient is
bounded from the non-zero vacuum expectation value of the Z-boson.
