A futures contract does not track one bond; it tracks a basket, and the short picks. Each eligible bond gets a conversion factor that standardises its coupon to the contract's notional coupon, but the factors are imperfect, so one bond is always cheapest.
The futures price behaves like the CTD bond, so its dv01 and duration are the CTD's. When yields move far enough the CTD switches, and the contract's risk profile changes with it. That optionality is why futures carry slight negative-convexity for the long.
Example: two deliverable bonds cost 99.12 and 99.35 after adjusting by their conversion factors. The 99.12 bond is cheapest to deliver, and the futures contract will track its price and yield.
Related: treasury-futures, dv01, negative-convexity