Later, gunmen attacked government targets and churches near the border with Cameroon, killing five policemen.
It is not yet clear who was behind the attacks.
But the army suspects the Islamist Boko Haram group, which often targets security forces, government officials or Christians it views as infidels.
Late on Saturday night, residents say a group of men went from house to house in a largely Christian area of the remote village of Chibok, before slitting the throats of 10 people.
"Suspected Boko Haram came at night and set people's houses on fire before killing their victims," Nuhu Clark, a former councillor of the village who escaped the attack, told Reuters news agency. He said he counted 10 bodies.
Porous border
On Sunday, residents of Gamboru Ngala near the border with Cameroon said gunmen killed five policemen as they attacked a police station, immigrations and customs offices, as well as at least one church.
A police spokesman said it had been very difficult to obtain information as some of the mobile phone masts had previously been destroyed by Boko Haram.
Boko Haram is not behind all the violence in northern and central Nigeria, says the BBC's Will Ross in Lagos, and armed groups are known to operate near the porous border with Cameroon.
But it is clear that the police and army are unable to protect people against widespread and frequent attacks, adds our correspondent.
Human rights groups say that more than 3,000 people have been killed by Boko Haram since 2010.
The group is fighting to overthrow the government and impose an extreme form of Sharia, or Islamic law.
