This paper proposes observability and measurement criticality analysis methods for any type of current phasor measurement configurations. Measurement Jacobian cannot be decoupled when using current phasor measurements and thus conventional methods of network observability analysis can no longer be used. Current phasor measurements may be classified into two types based on their configuration. Depending on whether there is a voltage phasor measurement at the sending end of the measured line or not, a current phasor measurement configuration may be referred to as of type-1 or type-2, respectively. Two methods which can handle conventional as well as phasor measurements, one being a modified version of the conventional method for type-1, and the other being a new method for type-2 phasor measurements, are developed and presented. Moreover, due to the fully coupled model used in the analysis, a method to handle voltage magnitude measurements is also developed.