On private property, including your own driveway, no City placement permit applies to the container.
The City's own container rules do reach you, and one clause runs in your favor. Middletown requires permanent on-site dumpsters to be screened from view behind substantially opaque enclosures of between six and nine feet, with a locking gate at business and commercial premises, and then says in terms that temporary dumpsters are excluded from that requirement. A container on a renovation is a temporary unit, so the screening rule does not bite.
For the street, Middletown has a route but it is a discretionary one. Placing material in a City street is prohibited except under permission from the Commissioner of the Department of Public Works, which the code gives in his or her sole discretion. That permission cannot run longer than six months, cannot obstruct a sidewalk, crosswalk or gutter, and cannot take up more than a third of the roadway opposite the property. It is revocable at any time, and everything placed under it has to be removed by the expiry date or on revocation. In practice that means a street placement in Middletown is a conversation, not a form.
One more City rule is worth knowing for a commercial address. The City gives each commercial property one free set of its own receptacles, but only if the property is not using a City-collected dumpster, and no property may use more than eight receptacles without written authorization from the Commissioner of Public Works. Only City-provided receptacles may go out at the curb, and everything must be off the curb by 7:00 p.m. on pickup day.
Call the City of Middletown at 845-346-4100 for the Department of Public Works. Your account manager can tell you whether your placement needs that permission at all.