There’s no law governing this. Depends on what the Democratic Party does. May be that it’s decided internally on Harris. No way to know for certain.
I expect that we will find out soon, because whoever runs has very little time to do so, so the Democrats cannot screw around here – they need to get a pick in place quickly and get the campaign moving.
Gretchen Whitmer and Gavin Newsom, the other two frontrunners I’ve seen mentioned, have previously said that they will not run against Harris if she wants it. So it’s probably Harris’s call.