Droplets formed in He-4 free jets expanded from source stagnation states in the vicinity of the critical point (T-c=5.2 K, P-c=2.3 bar) are investigated using a mass-spectrometer time-of-flight (TOF) technique. Depending on the source conditions, three different TOF peaks are identified : (a) atoms, (b) droplets formed by condensation from the gas phase, and (c) droplets formed by disintegration of the liquid phase. The latter show the lowest ever observed He-4 cluster speeds, about 50 m/s, at a source pressure of 1.5 bar and a source temperature of 4-5 K, just below the critical pressure and temperature. The TOF distributions at the critical point are very broad and this may be due to critical-point fluctuations during the averaging period (2-10 min) of the individual measurements.