Almost always, it is the landlords who are responsible for cutting trees, cleaning branches, etc. The only usual exceptions are either (1) where a lease says it's the tenant's responsibility; or (2) if the entire propery, including the yard, is rented to a single tenant (e.g. renting a single family home to one tenant or one family)--because then the assumption is that if the tenant rents the entire  property, he or she is responsible for basic clean up, as tenant is resonsible for keeping his/her apartment clean. However, in multiple tenant situations, or even a single tenant one where the tenant does not have possession and control over the yard, it would almost always be the landlord who is responsble for all "yard" or "landscaping" work and maintenance, even clean-up. Even in a single tenant renting the whole property situation, while the tenant might be responsible for routine outdoor clean-up, such as picking up fallen branches, the landlord would still be responsible for cutting or removing trees unless the lease said otherwise, the same way thhe landlord is generally responsible for "capital expenditures," such as repainting the premises or repairing wind damage to the building.