I am amazed that you are being asked to request a statutory assessment without any guidance. If you are a pre-school setting you need to contact your Area Senco for advice, if you are in a school, your Senco should already know.
I was an Area Senco so have helped lots of settings with requests, and that is what you have to remember - it is a request to the LA and it is their decision whether a statutory assessment is appropriate or not. LAs vary on their criteria for carrying out an assessment and if they issue statements at all, as most give schools a budget for supporting children with SEN and some give more than others. A few LAs do not do assessments at all.
Nearly all have a form to use for the request, which needs to be completed as fully as possible. That is where the Area Senco advice comes in. All authorities I have known also require you to send in with the form evidence of the child having Individual Education Plans at Early Years Action Plus for a minimum of 6 months, which show the child still has not made progress despite this support. Also I have always advised that the more professionals you have 'on board', the more likely the LA to carry out an assessment - so get everyone you can think of to come and observe, so the list of external agencies is as long as possible.
I notice other posts have talked about being negative. It is true that you do have to write clearly and specifically what the needs of the child are and this does not come naturally (and can be very hard for parents to read). But you do still need to be honest!
You need to be sensitive to parents through this process and not promise anything. It is the LA who decide if an assessment is needed and they also decide if they should issue a statement, you cannot make that decision nor can the parents.
Hope you are getting the help you need.