Face attributes are represented as human-interpretable visual characteristics in facial images, and the accurate recognition of facial attributes is regarded as the foundation for human-robot interaction in embodied robots. To enable the simultaneous recognition of facial expressions, facial features, skin tone, age, and other facial attributes, a state space model-based deep multi-task learning method for face attribute recognition (SSM-FAR) was proposed. Firstly, ConvNext's capability to encode local image features was leveraged in SSM-FAR, so that fine-grained image features were fully encoded by the backbone network for facial attribute recognition. In addition, a feature fusion module was employed to enhance the model's ability to recognize multi-scale and complex features. Secondly, a feature enhancement module based on the state space model was utilized to compensate for the backbone network's inadequacy in encoding global features. Our method reached accurate classification of facial expressions and the remaining 40 facial attributes in multi-task for face attribute recognition. Experimental results show that average accuracy rates of 91.70%, 86.73%, 91.23% and 66.51%are achieved on the CelebA, LFW-A, RAF-DB, and AffectNet datasets, and that SSM-FAR outperforms all compared state-of-the-art methods.