In general the owners of single-family homes have fewer legal responsibilities than renters do. However, they have more financial responsibilities.
Renters have entered into leases that spell out their responsibilities. They must generally, for example, maintain their homes in a condition that is similar to that in which they found it. For example, they can typically be penalized if they cause damage to walls or if they leave an apartment in a state in which the landlord deems that it needs to be cleaned. Home owners have no such legal responsibilities. People who own their own homes can make holes in the walls if they want to. They do not need to have the home clean when they leave. These are things that are up to them.
However, owners have financial responsibilities. If the toilet breaks in an apartment, the landlord is generally responsible for fixing it. If you own your own home and the toilet breaks, you must pay to fix it. In other words, the financial responsibility for the upkeep of the home is yours.