In this work we consider the dynamics of two tunnel-coupled chains after a quench in the tunneling strength is performed and the two systems are allowed to evolve independently. We describe the form of the initial state, comparing with previous results concerning the dynamics after the splitting of a one-dimensional gas of bosons into two phase-coherent systems. We compute different correlation functions, among which are those that are relevant for interference measurements, and discuss the emergence of effective temperatures also in connection with previous works.