Yes, usually.

On p. 101, it explains what happens when you get a new Hate:

> ...Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98)

> ...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.