Salahuddin provincial spokesman Mohammed al-Asi said the two explosions went off outside the state-run Rafidain bank where policemen were picking up their monthly pay. It wasn't known how many policemen were among the dead and wounded.
Television footage of the blast showed a huge white mushroom cloud over the two-story bank, followed by thick black smoke. A car parked nearby was on fire, and firefighters struggled to douse the flames. Iraqi security forces sealed off the area.
Another provincial spokesman, Ali Abdul-Rahman, said at least 12 people were killed. Al-Asi confirmed the death toll and said 34 people also were wounded.
Tikrit, 80 miles (130 kilometers) north of Baghdad, has been at the epicenter of deadly strikes on Iraq's government in the country's north so far this year.
In June, a suicide bomber attacked a mosque filled with Iraqi politicians and policemen while another blew himself up inside the hospital where the wounded were taken, killing a total of 21 people.
In March, gunmen strapped with explosives stormed the provincial council building and held off Iraqi forces for five hours before blowing themselves up. Fifty-six people were killed, including 15 who were shot execution-style in the head.
And in January, a suicide bomber killed 52 people among a crowd of police recruits in Tikrit. The bomber had joined hundreds of people waiting outside a police station to submit applications for 2,000 newly created jobs.
The attacks reflect the difficulties Iraqi security forces face in protecting their own people from Sunni insurgents still intent on undermining the country's post-Saddam leaders, many of whom are Shiite. Such violence is all the more troubling because of the approaching year-end deadline for American forces to leave.
In Washington, Vice President Joe Biden will chair a private meeting with advisers Thursday to discuss Iraq, following a Wednesday night phone call to Iraqi Prime Minister Nouri al-Maliki.
In a statement, al-Maliki said he told Biden that Iraq's leaders may soon reach agreement on whether to ask U.S. troops to stay on beyond the year's end, but the final decision is up to parliament.
All U.S. forces are required to leave Iraq by Dec. 31 under a 2008 security accord between the two countries. But many officials from both nations believe Iraq is still too unstable to protect itself without U.S. help, and Washington has offered to let up to 10,000 U.S. troops stay to train the country's security forces.
Al-Maliki "stressed that the Iraqi parliament is the body that decides eventually whether the country needs the U.S. forces to stay or not," the statement said. Al-Maliki also told Biden that "the leaders of the political blocs might be able to reach a decision on this during their next meeting."
However, a large and continued presence of U.S. troops may be difficult to sell to an Iraqi public already tired of eight years of war.
Moreover, if the troops stay, al-Maliki risks a potentially violent backlash from the followers of the anti-American cleric Muqtada al-Sadr, who has galvanized grass roots support across Iraq by promising to drive out the U.S. military.
With the U.S. troop presence a hotly contested issue, al-Maliki wants parliament to be responsible for the final decision.