The existence of the critical point(CP) of strongly interacting matter is still an open problem. An extensive strong interactions program including search of the CP and study of the onset of deconnement was started by the NA61/SHINE at SPS at CERN. Two dimensional phase diagram scan is expected to give more insight into the CP location and to shed the light on the phase transition region. This program includes studies of hadron production in proton-proton, proton-nucleus and nucleus-nucleus interactions measured in wide range of colliding energy and system size. Correlations between various observables measured at midrapidity as well as in separated rapidity intervals are considered as an additional and sensitive tool of this phase diagram scan. We present here the NA61/SHINE correlation program: the results of studies of the energy dependence of two-paticle correlations of transverse momentum and multiplicity in p+p and Be+Be collisions measured at the SPS and the first results on correlations between observ