In this work, we consider distributed adaptive learning over multitask mean-square-error (MSE) networks where each agent is interested in estimating its own parameter vector, also called task, and where the tasks at neighboring agents are related according to a set of linear equality constraints. We assume that each agent knows its own cost function of its vector and the set of constraints involving its vector. In order to solve the multitask problem and to optimize the individual costs subject to all constraints, a projection based diffusion LMS approach is derived and studied. Simulation results illustrate the efficiency of the strategy.