Pretty sure it depends on the states health dept. Several states require the reporting of differetn dz such as STD's and TB, but once you contact them, they take over w/notifying the family and others. At least in my experience in the ER the Health Dept really works w/the patient and at the least can send out a letter to those thought to be exposed that is generalized and anonymous which would be like "It has come to our attn that in the previous X months you may have come into contact w/ an individual that has tested positive for X. Sites/resources for further testing...."
Also, I randomly found out that if a pt is + for certain dz's and refuses to take medication on schedule, a judge can legally have them thrown in jail for propigating a dz, or at least in Ohio.
As far as a pt refusing to help at all, it depends on the state law, which range from nada, to jailtime for sexual contact, to being held in a kind of contempt. All this depends on every states law.