Property Management liability insurance

[Mark Ham]

So I have been asked to put the PM as a co-insurer on my policy, but when I ask whether they have any liability insurance, I didnt get a clear answer.  Is this a red flag?  When will a situation when there is a lawsuit against me vs the PM or both?  

Also, how much landlord liability is generally sufficient?  Understand that's is YMMV, the property is worth between $150k to $200k.