When responsibility is disputed

What to establish, in order

1. What does the operating authority’s published rule say, in its own words?
2. Where is the condition, measured from what reference point, and by whom?
3. Does the authority hold a record showing the connection or the boundary for this address?
4. What exactly has each party stated, and is any of it in writing?
5. Is there a stated deadline on any notice, and what does the notice say satisfies it?
6. Does the authority have a written review or appeal process?

Keeping the question open

The pressure in a dispute is to resolve it by paying, because the work is needed and the argument is exhausting. That is sometimes the right call. It is worth making it deliberately rather than by default.

If you do proceed with work while responsibility is unresolved, record that fact explicitly: what was unresolved, what each party had stated, and on what date. Work performed does not retroactively establish who owed it, but a record made at the time is much easier to rely on than one reconstructed later.