  In this paper, we show several rigidity results for harmonic $(p,q)$-forms in
complete K\"{a}hler manifolds. We also give several applications to study
non-compact K\"{a}hler manifolds with parallel Bochner tensor or quaternion
K\"{a}hler manifolds. Our results are natural extensions of Petersen and Wink's
results in \cite{PW21, PW} in the setting of complete, non-compact K\"{a}hler
manifolds.
