Swagger Response Body require object if property equals a value OpenApi Spec 3

It's possible but cumbersome. You need to use anyOf, like this:

CheckResponse:
  type: object
  required:
    - check_completed
  properties:
    check_completed:
      type: boolean
    check_details:
      $ref: '#/components/schemas/checkdetails'
  anyOf:
    - properties:
        check_completed:
          enum: [false]
    - properties:
        check_completed:
          enum: [true]
      required:
        - check_details

I would recommend describing this dependency in the schema/property descriptions instead.

OpenAPI 3.1 (future version) will make this easier thanks to using the latest JSON Schema which includes if...then..else among other things.

CheckResponse::
  type: object
  required:
    - check_completed
  properties:
    check_completed:
      type: boolean
    check_details:
      $ref: '#/components/schemas/checkdetails'
  if:
    properties:
      check_completed:
        const: true
  then:
    required:
      - check_details