Methods and apparatus to detect leakage current in a resistance temperature detector are disclosed. An example method includes providing a resistance temperature detector circuit with a first resistance circuit and a second resistance circuit, measuring a first voltage at the first resistance circuit in response to applying a first current to the first resistance circuit, measuring a second voltage at the second resistance in response to applying a second current to the second resistance circuit, comparing the first and second voltages to determine a difference value, and determining that a current leak exists in the resistance temperature detector circuit when the difference value is not within a first range.