In QGIS there is a toolbox, you will need to open this. Go to Processing menu and select toolbox.
It is really good to have a unique attribute on the polygons to allow attribute joining at the last step, to do this if you don't already have one, add a field and field calculate to $rownum:
To convert polyogns to centroids use the polygon centroids tool:
This will put a point roughly in the centre of each polygon with all of the attributes from the polygon (if you have a unique identifier this would be great).
Then intersect the centroids with the PLUTO layer:
Which will add the attributes of the polygon in the PLUTO layer that the point (centroid) falls in.
To get the attributes from the intersected centroids back to the building polygons either Attribute Join if you have a unique identifier for the buildings or Spatial Join if there is no unique identifier. In an attribute join open the attribute table and field calculate, the joined records will have the layer name and an underscore before the fields.
As was mentioned earlier the centroid will only match with one polygon in your PLUTO layer; if the building is across two PLUTO polygons it will only have the value of one of these polygons.
Warning centroids are not guaranteed to be within polygons. In certain rare instances the centroid may fall outside (Thanks for reminding me about that ChrisW):
There is a suggested workaround involving creating random points but this would introduce new problems. I suggest intersecting the centroids with the buildings and anywhere where the unique IDs don't match fix manually by moving the centroid to the visual centre of the building but well inside. Normally the number of points on man-made features that would need to be edited is around 1%; people tend to build boxes, only rare instances have voids or are unusually shaped enough for the centroid to fall outside. Natural features on the other hand you can expect to edit between 10 and 50 percent as the shapes tend to be more organic.