That's not true.This shows a profound misunderstanding of the structure of the United States of America. It is a union of STATES. The Constitution specifically mentions states. Not counties nor cities. The Constitution identifies the Federal, States and the People as each having specific powers. It also specifically states that those powers that are not specifically enumerated in the Constitution to the Federal government are reserved for the States or the People as stated in Amendment X. The power to regulate abortion is not a power granted to the Federal government by the Constitution.
The word "abortion" doesn't appear in the Constitution, but the 14th Amendment establishes that no State shall deprive any person within its jurisdiction the equal protection of the laws and gives Congress the power to enforce this provision.
Denying the right to bodily autonomy to pregnant people violates this equal protection clause. This was acknowledged in the Roe v. Wade decision.