We supply materials to subcontractors, and we sent a notice of furnishing thinking the job was privately-owned. Turns out the job is owned by the county. Do I need to send another notice of furnishing that is public-specific? We are now past the 21 day deadline. Thanks.
On a public project, only the principal/prime/general contractor must be served with a notice of furnishing, so from the facts you offered up, you properly served the principal.
For future reference as well, notices of furnishing relate back 21 days as well, so even if you are late, it makes sense to serve one later in the project, because it may just be your last 2 pay apps that are in dispute, so even if you served your notice of furnishing late, but before your last 2 pay apps, you would have a properly served notice of furnishing in that scenario.