have a look at the API documentation for QgsZonalStatistics. There is stated, that you can use flags to indicate which statistic you want to include. A complete list can be found in this section.
So you would do something like this:
myRasterLayer = 'C\path\to\raster\my_raster.tif'
QgsZonalStatistics(myPolyLayer, myRasterLayer, "prefix", 1, stats = Statistics( Count | Sum | Mean| StDev) )
Where myPolyLayer is your input Polygone, myRasterLayer is the path to your raster file from which you want to get the statistics, prefix a prefix for your attributes (can be empty), 1 stands for the rasterband you are looking in and stats determine the flags.