States in the N = 35 and 37 isotopes Ca-55,Ca-57 have been populated by direct proton-induced nucleon removal reactions from Sc-56,Sc-58 and Ca-56 beams at the RIBF. In addition, the (p, 2p) quasi-free single-proton removal reaction from Ca-56 was studied. Excited states in K-55, Ca-55, and Ca-57 were established for the first time via in-beam gamma-ray spectroscopy. Results for the proton and neutron removal reactions from Ca-56 to states in K-55 and Ca-55 for the level energies, excited state lifetimes, and exclusive cross sections agree well with state-of-the-art theoretical calculations using different approaches. The observation of a short-lived state in Ca-57 suggests a transition in the calcium isotopic chain from single-particle dominated states at N = 35 to collective excitations at N = 37.