Is a Catholic required to go to confession at least once a year if he has not committed a mortal sin?

No. Church law requires confession only of grave (mortal) sins at least once a year. If a person has committed no mortal sins, he is not obligated to go to confession. The Code of Canon Law states:

After having reached the age of discretion, each member of the faithful is obliged to confess faithfully his or her grave sins at least once a year. (CIC 989)

That said, “it is recommended to the Christian faithful that they also confess venial sins” (CIC 988).