The sharp-edged weapon with which 35-year-old Shailza Dwivedi, wife of another Army Major, was killed, though her body is yet to be recovered, they added.
Police will be taking the accused, Major Handa, to Meerut in –order to recreate the sequence of events and to ascertain where he could have thrown the knife he used to slit the woman's throat.
On Wednesday, the accused was taken to some places in southwest Delhi to identify the places where he could have thrown the knife, police informed.
Police also spoke to the family members of the accused whether they had any inkling of his plan to kill the woman.
The 40-year-old accused was arrested from Uttar Pradesh's Meerut on Sunday for killing the woman. According to the police accused major was obsessed with the lady and wanted to marry her.
Her persistent denial drove the major to kill the woman.
Later , her body was found with her throat slit near the Brar Square in the Delhi Cantonment area on Saturday.
Initially, the police was informed that a woman had died in an accident. Later, when they inspected the body, it was found some foul play since her throat was found slit.
It is said that the accused had allegedly run his car over her face and the body in order to make the incident appear as an accident. The woman was dropped at the Army Base Hospital in her husband's official vehicle by a driver on Saturday.
Later, when the driver came back to pick her up, he could not find her and learnt that she did not attend her scheduled physiotherapy session.