In the US the decision of who pays for which utilities is agreed upon by the tenant and landlord and spelled out in the lease agreement.

In most cases the decision is based on how the unit is metered. If each unit has a separate meter then usually the tenant pays the bill. If there is one meter for multiple units then the owner pays the bill.

Regardless of the meter, in some cases the owner may choose to pay the bill and re-bill the tenant. In some jurisdictions, the utility provider may be able to impose a lien on a property if the bill goes unpaid. This is very common for water / sewage service. The issue is if the tenant doesn't pay the bill, then the utility then places a lien on the property. Some jurisdictions have strict rent control laws and so the tenant could go for years without paying the bill and the lien could be quite large.