We report on the results of the cross-correlation of a sample of 903 Ultraluminous IRAS galaxies (ULIRGs) with the ROSAT-All Sky Survey Bright Source Catalogue and the ROSAT archived pointing observations. The sample of ULIRGs has been compiled from the PSCz redshift survey. In total, 35 ULIRGs are securely detected by the ROSAT All-Sky Survey and pointing observations, five of which are blazars. The statistical properties of these sources in the soft X-ray band are determined and compared with their properties in other wavebands. We find that the ratio of the soft X-ray to the far-infrared flux spans about 5 orders of magnitude and reaches values of about unity. This ratio is a good indicator of the main energy source of ULIRGs. Those with soft X-ray to far-infrared flux exceeding 0.01 are probably powered by accretion onto central supermassive black holes while those with ratios smaller than 0.001 are probably caused by starbursts or other heating processes, or are Compton thick sources. Some ULIRGs have energy contributions from both. This ratio is low for most ULIRGs and hyperluminous infrared galaxies, which explains their low detection rate by ROSAT and ASCA. We also find that some ULIRGs have a similar soft X-ray luminosity vs. temperature relation to that for groups of galaxies and elliptical galaxies, suggesting a common origin of these systems. Our study also reveals a correlation between the hardness ratio and the soft X-ray luminosity for Seyfert 1s/QSOs.