Assessment in the Indian population is more relevant here. There are these instruments which is used clinically and for research. It has two languages. English and Hindi.
NIMHANS battery for Specific learning Disability in English and Kannada.
Dyslexia Assessment for Languages of India (DALI) . DALI standardized test to detect dyslexia is available in four regional Indian languages – Hindi, Marathi, Kannada, and English. Work is underway to standardize in Telugu. Tamil and Bengali.
Both are downloadable. Better to Contact Child Psychiatry unit at Institute of Mental Health, Vizag.
As far as I know, the idea to assess reading and understanding of written langage relies on standardised tools which are designed according to the language used at school. For instance, in our bilingual population coming from UK or Germany and living in France, we use either tools designed for the main language used in school, either French if so, or according to the corresponding language. Indeed, if there is no specific learning disability, a double language exposure does not represent an extra burden, either for oral as well as for written language. We have the same situation for kids from a double cultural setting, with arabic language teached at school as they live in France: the reading assessment relies on the standard tests used commonly for native French students.