We propose a novel method for testing the null hypothesis of no effect of a covariate on the response in the context of functional linear concurrent regression. We establish an equivalent random effects formulation of our functional regression model under which our testing problem reduces to testing for zero variance component for random effects. For this purpose, we use a one-sided score test approach, which is an extension of the classical score test. We provide theoretical justification as to why our testing procedure has the right levels (asymptotically) under null using standard assumptions. Using numerical simulations, we show that our testing method has the desired type I error rate as well as a higher power than the bootstrapped F test currently existing in the literature. Our model and testing procedure are shown to give good performances even when the data is sparsely observed, and the covariates are contaminated with noise. We also illustrate our method by applying to two real data applications: the gait data and dietary calcium absorption study data.