This paper proposes a novel approach to detecting the topology of distribution networks based on the analysis of time series measurements. The analysis approach draws on data from high-precision phasor measurement units (PMUs or synchrophasors) for distribution systems. A key fact is that time-series data taken from a dynamic system show specific patterns regarding state transitions such as opening or closing switches, as a kind of signature from each topology change. The algorithm proposed here is based on the comparison of the actual signature of a recent state transition against a library of signatures derived from topology simulations. The IEEE 33-bus model is used for initial algorithm validation.