We present the results of a systematic search for molecular outflows in 68 Very Low Luminosity Objects (VeLLOs) from single-dish observations in CO isotopologues, finding 16 VeLLOs that show clear outflow signatures in the CO maps. Together with an additional three VeLLOs from the literature, we analyzed the outflow properties for these 19 VeLLOs, identifying 15 VeLLOs as proto-brown-dwarf (proto-BD) candidates and 4 VeLLOs as likely faint protostar candidates. The proto-BD candidates are found to have a mass accretion rate (~10-8--10-7 Msun yr-1) lower than that of the protostar candidates (？10-6 Msun yr-1). Their accretion luminosities are similar to or smaller than their internal luminosities, implying that many proto-BD candidates might have had either small accretion activity in a quiescent manner throughout their lifetimes, or be currently exhibiting relatively higher (or episodic) mass accretion than in the past. Outflows of many proto-BDs show strong trends of being less active if they are fainter or have less massive envelopes. The outflow forces and internal luminosities for more than half of the proto-BD candidates seem to follow the evolutionary track of a protostar with an initial envelope mass of ~0.08 Msun, indicating that some BDs may form in less massive dense cores in a similar way to normal stars. But, because there also exists a significant fraction (about 40%) of proto-BDs with a much weaker outflow force than expected from the relations for protostars, we should not rule out the possibility of other formation mechanism for BDs.