Answer:
Yes. This is why most apartments or landlords require it. This is something that a lot of people overlook when renting. If someone is injured on your promises you are liable.
Most comprehensive tenant's policies include $1 million in personal liability, which is pretty standard. Liability coverage could also cover you when you are liable for damages off your premises. For example, if you served alcohol to your house guests and let them drive home impaired and they cause an accident that injured 4 people, you may also be held liable and your personal liability coverage would provide protection.