As a general rule, no, you do not have an obligation to tell your partner if you have a sexually transmitted disease. There arent any federal or state laws making it illegal for you to not tell a partner about an STD you may have.

Can someone sue me for giving them an STD?

In California, there are circumstances where you can sue the person who infected you with a sexually transmitted disease. There are even rare cases in which you can sue and not have been infected. A threat of exposure can be grounds for a civil lawsuit.