In nowadays, ohmic-contact MEMS switches have been widely studied due to their variously advantages, such as high isolation, low insertion loss, negligible power consumption and so on. The micro-contact behavior has been analyzed by several researchers using the conventional asperity deformation model, in which the electrical contact resistance decreases gradually with increasing contact force and finally reaches a saturation region. This paper presents a study of the instable region of micro-contact behaviors under low contact force and low current conditions, where the conventional model does not seems to be applicable. Random telegraph signals (RTS) were captured during the transition period before the establishment of stable electrical contact. An electrothermal approach was applied in our work and the time constants of the RTS during instable region are extracted statistically from the experimental data. The fundamental mechanism for the contact resistance instabilities were discussed under the framework of material transfer enhanced by localized Joule heating.