In the real life case Citizen X is inspired by[0], nobody was tortured for a conviction, even the guilty man, who was simply put into a cell with a police informer to gather information and questioned normally by investigators who only had ten days under Soviet law to release or charge him.
"At his trial, Kravchenko retracted his confession and maintained his innocence, stating his confession had been obtained under extreme duress."
As in that example with Kravchenko, the same way false confessions occur in every country, pressure in some form from the police who want to convict their prime suspect / clear up a case.
It's indefensible but it's nothing unique to the Soviet Union and it's not uncommon.
https://theconversation.com/suspects-confess-to-crimes-they-...