Local identifiability is studied of a depending on a parameter linear system of ordinary differential equations via observations of solutions in two points. It is supposed that for the system are fulfilled the uniqueness condition and that each solution is determined on a segment [O, T], T>0. The conditions are obtained for which the identifiability via two-point observation is equivalent to identifiability via observation of solutions on a segment. Sufficient conditions of local identifiability via observation in O, T are formulated.