I could not find any tools that you could download and use, but perhaps something here might help?
The article below looks at various scales that might be of interest:
Petrucci, C., Marcucci, G., Carpico, A., & Lancia, L. (2014). Nursing care complexity in a psychiatric setting: results of an observational study. Journal of psychiatric and mental health nursing, 21(1), 79-86.
This article was written in 2007, and some of the measures listed date from quite a long time ago, but it might be worth looking at:
Abeles, P., Danquah, A., Wadge, M., Hodgkinson, P., & Holmes, E. (2007). Measuring patient dependency in child and adolescent mental health. British Journal of Nursing, 16(17), 1064-1072.
Mukai, H. A., Jericó, M. D. C., & Perroca, M. G. (2013). Care needs and workload required by institutionalised psychiatric patients. Revista latino-americana de enfermagem, 21(1), 340-347.
Thre are variants of the safer Nursing Care Tool developed for mental health settings. It is referred to here: https://hee.nhs.uk/hee-your-area/west-midlands/about-us/our-governance/our-letcs/mental-health-institute-letc/safe-staffing-tools-mental-health-learning-disability - although it suggests the link to the tool itself is available it isn't as far as I can see but there is a contact email for the authors.
Enclosed I have attached an article published by Fenneran et al., (2015) which explored the usability of the Safer Nursing Care Tool and the Mental Health and Learning Disability Workload Tool from the perspectives of nurses. Information related to the two tools is provided in the article. I hope this can be of use.