Is it necessary to offer any animal sacrifice during Hajj and at the same time at your native place?
If one is performing Hajj Tamattu or Qiran, it is necessary on her/him to do the Qurbani of hajj in the boundary of Haram. And if he stays in Makkah during those days then a separate Qurbani of Eidul Azha shall be wajib. One is free to do the Qurbani of Eidul Azha whether in Makkah or get it done at his native place.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband