We present a detailed Monte Carlo study of the many-particle density correlations in an interacting two-dimensional (2D) Bose gas, which are responsible for the recombination and spin relaxation rates in real experiments. We confirm that a 1/m! effect for local correlators does exist in 2D and can be used for the study of phase transitions. In agreement with a recent experiment [A. I. Safonov et al., Phys. Rev. Lett. 81, 4545 (1998)], the appearance and growth of quasicondensate fluctuations changes local correlations well before the Kosterlitz-Thouless transition point. Even a moderate interaction considerably reduces the amplitude of the 1/m! effect. This conclusion indicates that the enhancement of the 1/m! effect observed in the experiment by Safonov et al. cannot be ascribed to finite-interaction effects in a purely 2D system.