The resolutions would have required an amendment to North Dakota's Constitution to allow for direct payments to residents.
Backers of the measures say they were patterned after the Alaska Permanent Fund, which is that state's oil savings account. Each year, all men, women and children who have lived in Alaska for at least a year get a share of the fund.
North Dakota has its own tax fund that has more than $850 million in assets.
The Legacy Fund gets 30 percent of the state's oil tax collections. None of the money can be spent until 2017, and even then it takes a two-thirds vote of the Legislature to dip into it.