This paper addresses the issue of double-dipping in off-policy evaluation (OPE) in behaviour-agnostic reinforcement learning, where the same dataset is used for both training and estimation, leading to overfitting and inflated performance metrics especially for variance. We introduce SplitDICE, which incorporates sample-splitting and cross-fitting techniques to mitigate double-dipping effects in the DICE family of estimators. Focusing specifically on 2-fold and 5-fold cross-fitting strategies, the original off-policy dataset is partitioned with random-split to get separate training and evaluation datasets. Experimental results demonstrate that SplitDICE, particularly with 5-fold cross-fitting, significantly reduces error, bias, and variance compared to naive DICE implementations, providing a more doubly-robust solution for behavior-agnostic OPE.