We present an analysis of the power fluctuations in the statistical steady state of a passively mode-locked laser. We use statistical light-mode theory to map this problem to that of fluctuations in a reference equilibrium statistical physics problem and, in this way, study the fluctuations nonperturbatively. The power fluctuations, being noncritical, are Gaussian and proportional in amplitude to the inverse square root of the number of degrees of freedom. We calculate explicit analytic expressions for the covariance matrix of the overall pulse and cw power variables, providing complete information on the single-time power distribution in the laser, and derive a set of fluctuation-dissipation relations between them and the susceptibilities of the steady-state quantities.