You know Conrail started on 1 April 1976-- conventional wisdom is Amtrak took over Washington-New Rochelle at the same time.
The Northeast Corridor that now belongs to Amtrak was conveyed from Penn Central to Conrail on 1 April 1976. Conrail operated it, using Conrail crews on Amtrak trains. Conrail also operated what is now Metro North as the Metropolitan Region, including New Rochelle - New Haven.
On Conrail conveyance day, 1 April 1976, Amtrak wasn't set up to operate their own railroad. They created a Northeast Corridor organization from scratch, bringing in many officials from the Reading. Later in 1976 - I want to say September but I don't have the exact date - Amtrak assumed operating and maintenance responsibility for the Northeast Corridor from Conrail. Amtrak dispatched the trains, maintained the track and bridges, and supervised the operation. But the train crews were still Conrail employees.
Conrail also continued operating the commuter services for MTA, MBTA, SEPTA, New Jersey Transit and Maryland DOT. So you had Conrail passenger trains operating on Amtrak's railroad, just the reverse of what you would expect. Over the years Amtrak took over the train and engine employees, Conrail got out of the commuter business, and all the other changes evolved. I don't have a good reference on the exact dates, but I'm sure that someone here does.