Is it legal for your employer to ask you to provide proof or a police report for a family member's suicide?

It would be legal for them to just fire her for missing work. California is an at-will employment state, and I do not believe there are any special protections for bereavement leave, unless they are specific to your sister's company. It sounds like they are offering to accept the seriousness of your sister's situation, but since she is new they do not yet know whether they can trust her. In this case, if she provides the proof she will likely be allowed to keep her job; if she does not, her employer will probably assume she is lying (because why else would she refuse?) and fire her.

Attorney Pickard is right. The employer does not need justification to fire your sister and it looks like they simply want justification for not firing her. Best of luck to you. If you found this answer helpful, let me know by clicking the "thumbs-up" button at the bottom of this answer. It’s easy and appreciated. This response is intended to be a general statement of law, should not be relied upon as legal advice, does not create an attorney/client relationship and does not create a right to continuing email exchanges.