Can 勝手に決める by itself carry a negative connotation? As in, to add a selfish and careless tinge to ? Here, for instance: > Implying that such action (without taking any other context into consideration) would lead the other party to lose to the speaker? Thank you.

Depending on the situation yes, it can carry a negative connotation. It is especially easy to see this situation in school and love-related dramas where people are trying to make plans and there is a quarrel or disagreement over something and one of the parties gives up trying to give input.

> A
> B
> A
> B
> A
> B
> A **** <\--- Is now angry/fed up