> Which law in which State?
Leading with Washington, where I reside and work as a healthcare provider...
RCW 70.58A.100 (https://app.leg.wa.gov/rcw/default.aspx?cite=70.58A&full=tru...)
Specifically subsection 5:
> For an unattended live birth not reported under subsection (4) of this section, a report of live birth and an affidavit stating the facts of the birth must be filed with the department within ten calendar days of the live birth.
(whereby unattended means 'with no healthcare provider, midwife, or facility representative present or applicable'.)
(For bonus, RCW 70.58A.120 captures "delayed reporting of a live birth" and the "establishing of facts" around the birth.)
> How would they know for home birth
I was going to offer the comparison to driving, where "they" don't know you're driving without a license until there is some form of or need for government interaction. But I fear this will lead to some comment about traveling versus driving.
> and would they arrest the baby?
This is fatuous. "Depending on the state, the parents may be fined, charged with imprisonment, or have to face other legal consequences." (emphasis mine).