This paper presents an efficient statistical analysis method for periodically switched linear (PSL) circuits with normally distributed element values in the frequency domain. The method employs a First Order Second Moment (FOSM) method to estimate the mean and variance of the frequency response of PSL circuits. In addition, it utilizes a new multistep numerical Laplace inversion algorithm to efficiently calculate the zero-state and zero-input responses of PSL circuits. The method has been implemented in a computer program. The effectiveness and computational efficiency of the method are examined by comparing the accuracy and CPU time of the method with those of brute force approaches and Monte Carlo simulation on example circuits.