She will ask the Sole Survivor to share a drink outside the Dugout Inn which then leads to a speech check and her revealing that she is Henry's daughter. She then interrogates the player character on his whereabouts, followed by the player's choice of confessing to her that Henry had been killed, lie to her by saying he's alive or doing it while telling the truth when the Diamond City Blues quest is abandoned.
If the Sole Survivor can pass a speech check convincing her that either Paul Pembroke is lying to her, or that Paul is actually the killer of Henry Cooke, she will admit that she doesn't know who to believe. After a few game days some residents will comment on how Paul was gunned down by a random woman on the street, implying Colette chose to kill Paul. She can later be encountered in Goodneighbor and if spoken to, will accuse you of killing her father and turn hostile.
If Cooke is alive at the end of the quest and Paul is aware of this, the player may tell Colette they do not know where Cooke is. She will leave the conversation peacefully and some time later may be found at The Third Rail in Goodneighbor. Or if you made a 70-30 share with Paul or didn't inform Paul about Henry's plan to raid the chem lab, at some point when re-entering Diamond City she may confront the Sole Survivor saying that she has found it was them and then attempts to kill the Sole Survivor should they fail to convince her that Paul was lying to her or that the Sole Survivor doesn't know who killed Henry.
There's also a variation where one ambushes Trish and Nelson Latimer's chem deal with Henry Cooke, but without Paul Pembroke. Now, if Henry gets killed, there's no option to implicate Paul. In this case, one may be able to convince Colette that the Sole Survivor doesn't know her father that well, or that they haven't seen him recently. Alternatively, one can say they killed Cooke, in which case Colette may threaten to kill the Sole Survivor. Then a speech check may convince her that this will not bring him back, but might be the death of her.