Legal Question in Real Estate Law in California

If by "bad" you mean the old landlord gives the new landlord negative comments about you as a tenant, yes, of course he/she can do this, so long as the comments are truthful. Further, under Civil Code section 47(c), even a false negative comment would pass the test of legality (i.e., it would not be defamatory), if it were made without malice (as the term "malice" is defined in the context of the law of defamation). So, yes, bad references are lawful as a general rule between old and new landlords.