дача заведомо ложных показаний(A person who intentionally makes a false statement in a statutory declaration is guilty of an offense, the punishment for which is imprisonment for a term of 4 years – see Section 11 of the Statutory Declarations Act 1959.4uzhoj)
выступить с заявлением(made a statement in connection with – выступил с заявлением по поводуmysteriousuniverse.org • "In 1868, a Frenchman named Raud made a truly extraordinary statement regarding a monstrous, near-dragon-like snake seen in the California countryside, earlier in that very same year, and which was estimated to have an overall length of around forty feet."ART Vancouver)
заявить о своей непричастности к(to do or say something to show that you do not agree with the views or actions of someone with whom you had a connection. dissociate yourself from something I wish to dissociate myself from Mr Irvine's remarks. LDCE – АД)
лжесвидетельство(e.g., a judge found him guilty of making a false statement and he was sentenced to three years' probation and a $600 (£400) fine; BBC News Alex_Odeychuk)