Where the injury or sickness for which compensation is payable under § 45-19-1, was caused under circumstances creating a legal liability in some person other than the employer to pay damages in respect of the injury or sickness, the employee may take proceedings, against that person to recover damages, and the employee is be entitled to receive both damages and compensation; provided, that the employee, in recovering damages either by judgment or settlement from the person liable to pay damages, shall reimburse the city, town, or the state of Rhode Island by whom the compensation was paid to the extent of the compensation paid as of the date of the judgment or settlement, and the receipt of those damages by the employee does not bar future compensation. If the employee has been paid compensation under that chapter, the city, town, or state of Rhode Island, by whom the compensation was paid, is entitled to indemnity from the person liable to pay damages as previously stated, and to the extent of the indemnity, is subrogated to the rights of the employee to recover damages; provided, that when money has been recovered, either by judgment or by settlement, by the employee from the person liable to pay damages as previously stated, by suit or settlement, and the employee is required to reimburse the city, town, or state of Rhode Island by whom the compensation was paid, the employee or the employee’s attorney is entitled to withhold, from the amount to be reimbursed, that proportion of the costs, witness expenses, and other out-of-pocket expenses and attorney fees, which is the amount which the employee is required to reimburse the city, town, or state of Rhode Island by whom compensation was paid, bears to the amount recovered from the third party.