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Statistical downscaling methods require the stationarity assumption, that is, the statistical relationship between the grid-scale input and the observed precipitation does not change between present-day and climate change conditions. We implemented a skill score to test the stationarity assumption in two simple and popular statistical downscaling methods, quantile-mapping and the generalized linear model method Rglimclim, in downscaling precipitation in the eastern United States, and examined the sensitivity of the results of the stationarity test to different ways to construct cross-validation periods that differ in climate conditions. The Rglimclim method passed the stationarity test at slightly more stations than quantile-mapping and was less impaired by increase in the resolution of input data. But neither method can be reliably applied to downscale the whole marginal distribution or time series of precipitation at the 54 stations in the study region, and only passed the stationarity test at a few stations on the annual extreme precipitation. We also found that the number of identified non-stationary stations was sensitive to which criterion (chronology, precipitation, temperature, large-scale circulation indices) was used to construct the cross-validation periods, and whether one or several criteria for cross-validation periods were used. These results raise caution against using the two statistical downscaling methods that we examined in climate change impact studies without testing their stationarity assumption, and also point to the need for more research into how to choose cross-validation periods and stationarity metrics in order to maximize their relevance to the reliability of statistical downscaling methods under future climate change.