The terrorists wore police uniforms and used a police vehicle to enter the city, located 175 km (110 miles) north of Baghdad, police colonel Khalid Mahmoud told Reuters. He said there were around 10 attackers, including two suicide bombers.
A total of 31 bodies were taken to hospital, including 14 belonging to policemen, said Nawfal Mustafa, a doctor at the city's main hospital. The death toll rose in the morning as more bodies were found, belonging to civilians killed in their shops.
The attacks targeted a police checkpoint and the house of a police colonel, who was killed with four members of his family, officers said.
Two suicide attackers detonated their vests when surrounded by police, and three others were killed in separate clashes.
Five terrorists are thought to be hiding and Mahmoud said Tikrit authorities had declared a curfew on Wednesday. Sporadic gunfire could be heard in the morning.
The terrorists overran about a third of Iraq's territory nearly three years ago, capturing most Sunni Arab cities located north and west of Baghdad, including Tikrit.
Iraqi forces and Iranian-backed Shi'ite militias drove the terrorists away from Tikrit two years ago. Tikrit is the home region of Saddam Hussein, the former president toppled in the 2003 US-led invasion of Iraq.
(Reporting by Ghazwan Hassan and Ahmed Rasheed, Writing by Maher Chmaytelli, Editing by Catherine Evans, Larry King)