This paper derives testable implications of the identifying conditions that include the local monotonicity assumption and the continuity in means assumption for the local average treatment effect in fuzzy regression discontinuity (FRD) designs. Building upon the seminal work of Horowitz and Manski (1995), we show that the testable implications of these identifying conditions are a finite number of inequality restrictions on the observed data distribution. We then propose a specification test for the testable implications and show that the proposed test controls the size and is asymptotically consistent. We apply our test to the FRD designs used in Miller, Pinto, and Vera-Hern´andez (2013) for Columbia's insurance subsidy program, in Angrist and Lavy (1999) for Israel's class size effect, in Pop-Eleches and Urquiola (2013) for Romanian school effect, and in Battistin, Brugiavini, Rettore, and Weber (2009) for the retirement effect on consumption.