A writ has been filed in the Technology and Construction Court following years of wrangling between the council and the contractor.
Zurich Insurance is also named in the action because of a performance bond taken out on the project.
The council confirmed last month that it had set aside £6.5m for any legal fight with Nuttall if the dispute failed to reach a mediated settlement.
Construction on the transport scheme went £64m over the original £87m budget and was opened two years late.
The council believes it owes Nuttall the £87m original fee plus any differences for delays and alleged defects.
Nuttall said the project cost £151m to build and wants full payment while the council believes the contractor is liable for the overspend.
Nuttall has consistently declined to comment on the case but is believed to be fighting the claim.