Detecting spoofed utterances is a fundamental problem in voice-based biometrics. Spoofing can be performed either by logical accesses like speech synthesis, voice conversion or by physical accesses such as replaying the pre-recorded utterance. Inspired by the state-of-the-art \emph{x}-vector based speaker verification approach, this paper proposes a time-delay shallow neural network (TD-SNN) for spoof detection for both logical and physical access. The novelty of the proposed TD-SNN system vis-a-vis conventional DNN systems is that it can handle variable length utterances during testing. Performance of the proposed TD-SNN systems and the baseline Gaussian mixture models (GMMs) is analyzed on the ASV-spoof-2019 dataset. The performance of the systems is measured in terms of the minimum normalized tandem detection cost function (min-t-DCF). When studied with individual features, the TD-SNN system consistently outperforms the GMM system for physical access. For logical access, GMM surpasses TD-SNN systems for certain individual features. When combined with the decision-level feature switching (DLFS) paradigm, the best TD-SNN system outperforms the best baseline GMM system on evaluation data with a relative improvement of 48.03\% and 49.47\% for both logical and physical access, respectively.