We propose a complementary phase detection algorithm to enhance the capabilities of the multi-tone continuous wave (MTCW) lidar for single-shot simultaneous ranging and velocimetry measurements. We show that the phase of the Doppler-shifted RF tones and the amount of the induced Doppler frequency shift can be used to extract the phase and velocity information, simultaneously. A numerical case study and experimental work have been performed for the proof of concept. We show that the velocity resolutions are limited by frequency resolution and the ranging resolution is determined by the temporal resolution. Experimentally, we obtain 8.08 ± 0.8cm/s velocity measurement and 111.9cm range measurements with ±0.75cm resolution in a 6-tone MTCW lidar system.