It is shown that the KPSS test for stationarity may be applied without change to regressions with seasonal dummies. In particular, the limit distribution of the KPSS statistic is the same under both the null and alternative hypotheses whether or not seasonal dummies are used.
Jin, Sainan and Phillips, Peter C.B., "The KPSS Test with Seasonal Dummies" (2002). Cowles Foundation Discussion Papers. 1637.