Cassette tapes should never be placed in your curbside recycling.
The film tape is a "tangler" that gets wound around the processing machines at recycling facilities and can shut down a whole recycling operation.
There are some specialized plastics recyclers that may be willing to accept the hard plastic outer shell and recycle it for a small fee. You would be required to remove the film first. The film tape cannot be recycled and must be disposed in the trash. Call Northcoast Recycling Specialist in Wickliffe (440.943.6968) or Secure IT Asset Disposition Services in Mentor (440.332.5005). You can also recycle cassette tapes via GreenDisk.
If you choose not to use a specialized recycler for your tapes, place them in the regular trash for disposal.