The PRESS statistic has been in use in linear regression as a criterion for model selection. It is believed, in some respect, that PRESS residuals could be better substitutes of the unobserved errors than traditionally and commonly used least squares residuals. Some distributional properties like moments, coefficients of skewness and kurtosis of PRESS residuals are studied. These residuals are then used in tests for Normality and a Monte Carlo simulation experiment is reported in this paper which is designed to investigate the performance of PRESS residuals in Normality test under a variety of error distributions.