This paper presents Communication efficient REcursive Distributed estimatiOn algorithm, CREDO for networked multi-agent systems. CREDO caters to situations in which the agents collaboratively estimate a vector parameter by assimilating their latest sensed information and estimates from their time-varying neighborhood worker nodes over a (possibly sparse) communication graph, while adhering to a frugal communication scheme. The underlying inter-agent communication protocol is randomized and adaptively, making communications increasingly (probabilistically) sparse as time progresses. CREDO may be designed to achieve at each agent a Θ(Ct^-2+ζ) decay of the mean square error ( , arbitrarily small) with respect to per-node communication cost Ct, which significantly improves over the existing Θ(Ct^-1) rates. Simulations demonstrate CREDO 's communication efficiency.