In the US you can, and I'd be surprised if many other jurisdictions saw it differently. In the US you have a right against self incrimination, not a right to lie and misdirect. See Martha Stewart as an example, part of her conviction was making false statements to an investigator.
Martha "Stewart was found guilty in March 2004 of conspiracy, obstruction of an agency proceeding, and making false statements to federal investigator". The lying to investigators was most of her "crime". If she'd told them to talk to her lawyer and clammed up, she'd have been way ahead. The Feds never did prove securities fraud.