The dependence of correlations of neutron multiplicity ν and γ-ray multiplicity Mγ in spontaneous fission of Cf252 on fragment mass A∗ and total kinetic energy (TKE) have been investigated by employing the ratio of Mγ/ν and the form of Mγ(ν). We show for the first time that Mγ and ν have a complex correlation for heavy fragment masses, while there is a positive dependence of Mγ for light fragment masses and for near-symmetric mass splits. The ratio Mγ/ν exhibits strong shell effects for neutron magic number N=50 and near doubly magic number shell closure at Z=50 and N=82. The γ-ray multiplicity Mγ has a maximum for TKE=165-170 MeV. Above 170 MeV Mγ(TKE) is approximately linear, while it deviates significantly from a linear dependence at lower TKE. The correlation between the average neutron and γ-ray multiplicities can be partly reproduced by model calculations.