We study conformal properties of local terms such as contact terms and
semi-local terms in correlation functions of a conformal field theory. Not all
of them are universal observables but they do appear in physically important
correlation functions such as (anomalous) Ward-Takahashi identities or
Schwinger-Dynson equations. We develop some tools such as embedding space delta
functions and effective action to examine conformal invariance of these local
terms.