Local frequency (LF) estimation of multidimensional (md) signals is considered. The md-Wigner distribution (WD) is used as the LF estimator. The LF is estimated based on the positions of the WD maxima. A nonparametric algorithm for the LF estimation is developed. It is based on the intersection of confidence intervals rule. This algorithm produces an adaptive window size in the WD which gives almost minimal mean squared error of the estimate. A simplified version of this algorithm is developed, with the starting estimate being produced with the WD of one-dimensional signals. Theory is illustrated in examples.