Due to the COVID-19 pandemic, automated contactless person identification based on the human hand has become very vital and an appealing biometric trait. Since, people are expected to cover their faces with masks, and advised avoiding touching surfaces. It is well-known that usually contact-based hand biometrics suffer from issues like deformation due to uneven distribution of pressure or improper placement on sensor, and hygienic concerns. Whereas, to mitigate such problems, contactless imaging is expected to collect the hand biometrics information without any deformation and leading to higher person recognition accuracy; besides maintaining hygienic and pandemic concerns. Towards this aim, in this paper, an effective multi-biometric scheme for person authentication based on contactless fingerprint and palmprint selfies has been proposed. In this study, for simplicity and efficiency, three local descriptors, i.e., local phase quantization (LPQ), local Ternary patterns (LTP), and binarized statistical image features (BSIF), have been employed to extract salient features from contactless fingerprint and palmprint selfies. The score level fusion based multi-biometric system developed in this work combines the matching scores using two different fusion techniques, i.e., transformation based-rules like triangular norms and classifier based-rules like SVM. Experimental results on two publicly available databases (i.e., PolyU contactless to contact-based fingerprint database and IIT-Delhi touchless palmprint dataset) show that the proposed contactless multi-biometric selfie system can easily outperform uni-biometrics.