You can't force the landlord to cut down the tree. However, if you provide him written notice (sent some way you can prove delivery--for example, fax, or registered mail with return receipt) that the tree is rotted and a hazard, you can later hold him liable for any damage or injuries the tree causes. That's because if the landlord is aware of a potential safety condition and refuses to address it, he may be liable for any harm that it causes.