Abstract: The N = Z = 36 nucleus Kr-72 has been studied by inelastic scattering at intermediate energies. Two targets, Be-9 and Au-197, were used to extract the nuclear deformation length, delta(N), and the reduced E2 transition probability, B(E2). The previously unknown non-yrast 2(+) and 4(+) states as well as a new candidate for the octupole 3(-) state have been observed in the scattering on the Be target and placed in the level scheme based on gamma – gamma coincidences. The second 2(+) state was also observed in the scattering on the Au target and the B(E2; 2(2)(+) -> 0(1)(+)) value could be determined for the first time. Analyzing the results in terms of a two-band mixing model shows clear evidence for a oblate-prolate shape coexistence and can be explained by a shape change from an oblate ground state to prolate deformed yrast band from the first 2+ state. This interpretation is corroborated by beyond mean field calculations using the Gogny D1S interaction.