Speaking strictly from a CPS standard, if this incident was called in directly as reported in the OP, it would have been screened out at intake - that is, not investigated. It was not directly witnessed, there was no visible injury, presumably the spanking was with an open hand and not an object, and it doesn't sound as though the parent had malicious intent to cause injury. Now, every Dept. has some variance about how they look at these types of calls, but it is very rare for our Dept. to intervene in a "spanking" report.
That's not to say the father wasn't a jerk because a crying child won't stop crying after a spanking; they cry harder, duh!
I have re-read the OP a couple of times now and still can´t see where it is clear that the little girl was spanked. Nobody was there to whitness it. The OP heard three "strikes" and we have no idea where they landed.