Were there laws against disbelief?

No, everyone was free to believe or disbelieve.

Now there was a strict law among the people of the church that there should not any man, belonging to the church, arise and persecute those that did not belong to the church, and that there should be no persecution among themselves. Alma 1:21

If a man desired to serve God, it was his privilege; or rather, if he believed in God it was his privilege to serve him; but if he did not believe in him there was no law to punish him. Alma 30:9

Yes, it was illegal to express disbelief.

What he had taught to the people was contrary to the word of God; and there he suffered an ignominious death. Alma 1:15

Now when the high priest and the chief judge saw the hardness of his [Korihor's] heart, yea, when they saw that he would revile even against God, they would not make any reply to his words; but they caused that he should be bound; and they delivered him up into the hands of the officers, and sent him to the land of Zarahemla, that he might be brought before Alma, and the chief judge who was governor over all the land. Alma 30:29