Hadron radiation therapy is of great interest worldwide. Heavy-ion beams provide ideal therapeutic conditions for deep-seated local tumours. At the Heidelberg Ion Beam Therapy Center (HIT, Germany), protons and carbon ions are already integrated into the clinical routine, while 16O ions are still used for research only. To ensure the protection of the technical staff and members of the public, it is required to estimate the neutron dose distribution for optimal working conditions and at different locations. The Particle and Heavy Ion Transport Code System (PHITS) is used in this work to evaluate the dose rate distribution of secondary neutrons in a treatment room at HIT where 16O ions are used: an equivalent target in soft tissue is considered in the shielding assessment to simulate the interaction of the beam with patients. The angular dependence of neutron fluences and energy spectra around the considered phantom were calculated. Alongside the spatial distribution of the neutron and photon fluence, a map of the effective dose rate was estimated using the ICRP fluence-to-effective dose conversion coefficients, exploiting the PHITS code's built-in capabilities. The capability of the actual shielding design of the studied HIT treatment room was approved.