Mumtaz Qadri, a member of Taseer`s security detail, gunned down the Governor in Islamabad on January 4.
He said he was angered by Taseer`s opposition to the country`s controversial blasphemy law.
Over 100 supporters of Qadri gathered outside Adiala Jail in the garrison city of Rawalpindi, where the case is being heard for security reasons, and shouted slogans.
A police draftsman and a constable recorded their statements during today`s hearing.
They told the court about the crime scene and Taseer`s autopsy.
Nearly two months after Taseer`s killing, Minority Affairs Minister Shahbaz Bhatti was assassinated by militants in Islamabad on Wednesday for challenging the blasphemy law.
The Taliban claimed responsibility for the killing of Bhatti, who was the only Christian member of the cabinet.