An official in the Ukraine Prosecutor's Office, Vadim Goran, denied her allegation, saying the bruises came from "pushing against blunt, hard objects, or banging into them" and "in no way resulted from a punch to the stomach as she says".
Ms Tymoshenko, a former prime minister and key rival of Ukraine's President Viktor Yanukovych, is serving a seven-year jail sentence for abuse of office and faces another trial on tax evasion charges.
The Office of Police Affairs says that since February 1997, it has received 20 separate requests from Ukraine for legal help in the case of Mr Lazarenko, and it has already handed over some bank documents to Ukraine.