Well how it works up here - it isn't just teachers who refer, in fact class teachers don't at all. But, if there's an underlying issue that hasn't been picked up pre-school the school doctor or nurse can refer either prompted by the class teacher, support for learning teacher or the parent.
For things like assessments or referral to an ed psych, again it's usually prompted by the class teacher, but if it isn't parents can request them.
Where it is fairly different though...my DS has fairly complex needs, but is no longer seen by any other agencies, SALT and OT have discharged him, so he doesn't qualify for a CSP, there's no-one else to co-ordinate so the school just get a free reign
anything in his IEP wouldn't be legally binding on their part, which is frustrating as children with less support needs would still qualify for one just because there is other agency involvement.