Can two birds of different species mate thus creating combined offspring?
There are many, many closely related species of birds that hybridize on a regular enough basis that their hybrid offspring have their own names in bird books. An example would be the blue-winged warbler and golden-winged warblers, which hybridize to produce Brewster’s and Lawrence’s warblers. However, these two warblers are very closely related, as is the case with all successful hybrids. The two parent species are often in the same genus, and always in the same family. The two birds you mention, a crow and a parrot, are not closely enough related to hybridize. They are only distantly related. I would suggest looking through some guides to your region – perhaps this is a bird with which you are not already familiar, or a plumage variant.