I'm not aware that in 1861 there was a federal law prohibiting secession; if there was it was not in pursuance of the original constitution.
For your conveinience: This Constitution, and the Laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the constitution or laws of any state to the contrary notwithstanding.
There wouldn't need to be.
The Supremacy Clause says that all state laws are subject to Federal review.
An "act of secession" is a declaration that no laws of the seceding state are subject to Federal review, which is a direct violation of the Supremacy Clause.