These are the reasons why, in the normal course of police work, they definitely would have wanted to discuss the Tippit shooting with Oswald and hear what he had to say about it and his involvement in it.
1. to find out if he had accomplices- obviously, very important. Or, could they just assume he was a lone nut in killing Tippit as well?
2. to find out where he was heading because obviously he wasn't going to the theater if he was at 10th and Patton
3. to find out why Tippit stopped him. Was it because of JFK or was it for some other reason? It pays to ask, doesn't it?
4. to hear his alibi if he denied killing TIppit. If his alibi could be proven false, that would cinch it.
5. to find out if he knew Tippit, if they had ever met before.
6. to find out if Tippit had tried to arrest him
7. to find out what specific thing Tippit said that provoked the violent attack by Oswald
So, all of that was hanging in the balance, yet there is NOT ONE WORD about the police discussing anything about the Tippit murder with Oswald. Not one word.