In a recent theoretical work, Phys. Lett. B785, 112 (2018), we proposed that a K * resonance with hidden charm content arises from the KDD * dynamics, where the DD * system is treated as a Z c (3900) or X(3872). With the motivation of determining its further properties, which can be observed in experiments, we now present a calculation of the decay processes of this K * , namely K * (4307), to two-body channels. Particularly, we consider the decay channels J/ψK * (892),DD s ,DD * s andD * D * s . The mechanisms of the decay to these channels involve triangular loops and are a consequence of the internal structure of the state. Thus, the values found for the decay widths of the proposed K * (4307) are related to its nature and should be valuable for carrying on an experimental study of the K * (4307). A K * state with such a mass (in the charmonium region) and quantum numbers is a clear manifestation of an exotic meson, since, having hidden charm (i.e., a cc pair), its mass and quantum numbers can not be explained within a quark-antiquark description.