Real-time hand movement trajectory tracking based on machine learning approaches may assist the early identification of dementia in ageing deaf individuals who are users of British Sign Language (BSL), since there are few clinicians with appropriate communication skills, and a shortage of sign language interpreters. In this paper, we introduce an automatic dementia screening system for ageing Deaf signers of BSL, using a Convolutional Neural Network (CNN) to analyse the sign space envelope and facial expression of BSL signers recorded in normal 2D videos from the BSL corpus. Our approach involves the introduction of a sub-network (the multi-modal feature extractor) which includes an accurate real-time hand trajectory tracking model and a real-time landmark facial motion analysis model. The experiments show the effectiveness of our deep learning based approach in terms of sign space tracking, facial motion tracking and early stage dementia performance assessment tasks