Dott, 47, who has been released on bail, is accused of two charges relating to young children.
The allegations span the period between 1993 and 1996 involving a girl, and 2006 to 2010 involving a boy, both in the Glasgow region.
Dott appeared at the High Court in Glasgow on Wednesday, and had his bail continued. He is expected to appear again on June 11.
Dott won the 2006 World Snooker Championship, and was runner-up in 2004 and 2010.
The World Professional Billiards and Snooker Association announced last week that Dott had been suspended due to the case.