Contactless fingerprint recognition systems offer a hygienic, user-friendly, and efficient alternative to traditional contact-based methods. However, their accuracy heavily relies on precise fingertip detection and segmentation, particularly under challenging background conditions. This paper introduces TipSegNet, a novel deep learning model that achieves state-of-the-art performance in segmenting fingertips directly from grayscale hand images. TipSegNet leverages a ResNeXt-101 backbone for robust feature extraction, combined with a Feature Pyramid Network (FPN) for multi-scale representation, enabling accurate segmentation across varying finger poses and image qualities. Furthermore, we employ an extensive data augmentation strategy to enhance the model's generalizability and robustness. TipSegNet outperforms existing methods, achieving a mean Intersection over Union (mIoU) of 0.987 and an accuracy of 0.999, representing a significant advancement in contactless fingerprint segmentation. This enhanced accuracy has the potential to substantially improve the reliability and effectiveness of contactless biometric systems in real-world applications.