Nick Brooks, son of accused rapist Joseph Brooks, penned an apology in the form of a letter to the woman he is accused of killing, the prosecution said yesterday.

ADA Jordan Arnold said at a court hearing that the letter, found in swimwear designer Sylvie Cachay’s purse, indicated that Brooks hadn’t accepted the end of their relationship.

Brooks, who was allegedly “shocked” to learn he was being charged with attempted murder and with strangling Cachay, was ordered held without bail until Thursday’s arraignment.

An autopsy said that Cachay’s wounds “were not self-inflicted or accidentally caused.”