  We present a systematic phenomenological analysis of the tests of CPT
symmetry that are possible within an {\em open} quantum-mechanical description
of the neutral kaon system that is motivated by arguments based on quantum
gravity and string theory. We develop a perturbative expansion in terms of the
three small CPT-violating parameters admitted in this description, and provide
expressions for a complete set of $K \rightarrow 2\pi, 3\pi$ and $\pi\ell\nu$
decay observables to second order in these small parameters. We also illustrate
the new tests of CPT symmetry and quantum mechanics that are possible in this
formalism using a regenerator. Indications are that experimental data from the
CPLEAR and previous experiments could be used to establish upper bounds on the
CPT-violating parameters that are of order $10^{-19}$ GeV, approaching the
order of magnitude that may be attainable in quantum theories of gravity.
