You probably have to file a Rhode Island nonresident return. As it is with most states, you are required to file RI if you are required to file the federal return and have any RI source income. A filing requirement doesn't mean tax will be owed, but the requirement to file will hit most taxpayers with RI source income, however small. There's no dollar amount for the RI income itself.
Under Personal Info, select Rhode Island as Other State Income. In the RI interview in Turbo Tax, you will allocate an appropriate portion of the net Schedule C income to the state.
http://www.tax.ri.gov/forms/2016/Income/2016%20NR%20Instructions_11302016.pdf
Source: Every nonresident individual required by the laws of the United States to file a federal income tax return who has income derived from or connected with Rhode Island sources must file a Rhode Island individual income tax return.
