This has been a particularly vexing question. First, it is well established that Constantine "legalized" Christianity in 313 AD. In doing so, it appears that Constantine granted specific rights to Christians regarding property and constructing churches. It's possible these specific rights were conferred by the Senate in the form of recognizing the Church as a collegium, but I can't seem to find that anywhere.
Additionally, what I can find about collegiums is that they were typically more related to "trade associations" of people, but not exclusively. When people used the legal vehicle for religious reasons it was often for a "funeral club." Assuming that collegiums for religious reasons were typically "funeral clubs," then I'm not sure why the Senate would take the time to recognize the whole christian church as a collegium, because it appears that collegia were normally established to buy a communal funeral plot of land.
Barring some additional sources, or direction, from the OP, I'm not sure how else to answer this question, other than it doesn't appear that the Senate would have even needed to issue such a thing. I can't seem to find anything that states that collegium was the sole legal person distinction recognized by Roman law (which makes sense), and as such the early Church could have been recognized under a different legal fiction.