Feynman-α analyses for a critical state and several subcritical states of the UTR-KINKI reactor have been carried out using two Bi14Ge3O12 (BGO) gamma-ray detectors free from radioactivation of the scintillator. As a statistical index of the analyses, the covariance-to-mean ratio of gamma counts between these detectors instead of the variance-to-mean ratio of each of the detectors is employed to get rid of a large negative correlation originating from the counting loss of a signal processing circuit. In the gate width dependence of the covariance-to-mean ratio measured at each reactor state, not only a familiar neutron-correlation component but also another small positive correlation between prompt gammas can clearly be observed. The prompt-neutron decay constant α determined considering the positive gamma correlation agrees very well with that obtained from a conventional Feynman-α analysis based on neutron detection. Neglecting the gamma correlation term, the decay constant is much overestimated with an increase in subcriticality, and the maximum overestimation reaches about 24% at a shutdown state with a subcriticality of 1.49%Δk/k.