Summary: We consider a class of linear time-periodic systems in which the dynamical generator \(A(t)\) represents the sum of a stable time-invariant operator \(A_0\) and a small-amplitude zero-mean \(T\)-periodic operator \(\epsilon A_p(t)\). We employ a perturbation analysis to develop a computationally efficient method for determination of the \(\mathcal H_2\) norm. Up to second order in the perturbation parameter \(\epsilon\) we show that: (a) the \(\mathcal H_{2}\) norm can be obtained from a conveniently coupled system of Lyapunov and Sylvester equations that are of the same dimension as \(A_{0}\); (b) there is no coupling between different harmonics of \(A_p(t)\) in the expression for the \(\mathcal H_{2}\) norm. These two properties do not hold for arbitrary values of \(\epsilon\), and their derivation would not be possible if we tried to determine the \(\mathcal H_{2}\) norm directly without resorting to perturbation analysis. Our method is well suited for identification of the values of period \(T\) that lead to the largest increase/reduction of the \(\mathcal H_{2}\) norm. Two examples are provided to motivate the developments and illustrate the procedure.