A connector includes a contact pin having an upper pin terminal and a lower pin terminal interposed between an upper connection object such as an IC or the like and a wiring substrate serving as a lower connection object so as to be brought into contact under pressure with contact pieces arranged on surfaces of the objects. The contact pin is held in a hole such that the contact pin as a whole can be moved upwardly and downwardly a predetermined stroke independent of resilient upward and downward movement of the individual upper and lower pin terminals. An upper movement preventive element and a lower movement preventive element, for establishing the upward and downward strokes, are formed between the contact pin and a wall of the hole. When the lower pin terminal is brought into abutment with the wiring substrate serving as the lower connection object, the overall contact pin is freely moved upwardly within the hole so as to engage the upward movement preventive element. After the completion of the engagement with the upward movement preventive element, only the lower pin terminal is push upwardly against the bias of the spring. When the upper connection object is brought into abutment with the upper pin terminal, only the upper pin terminal is descended while compressing the spring, thereby attaining electrical contact under pressure.