  In this study, we introduce a two dimensional complex harmonic oscillator
potential with space and time reflection symmetries. The corresponding time
independent Schr\"odinger equation yields real eigenvalues with complex
eigenfunctions. We also construct the coherent state of the system by using a
superposition of 12 eigenfunctions. Using the complex correspondence principle
for the probability density we investigate the possible modifications in the
probability densities due to the non-Hermitian aspect of the Hamiltonian.
