What is the correct way to check if a path is an UNC path or a local path?

Since a path without two backslashes in the first and second positions is, by definiton, not a UNC path, this is a safe way to make this determination.

A path with a drive letter in the first position (c:) is a rooted local path.

A path without either of this things (myfolder\blah) is a relative local path. This includes a path with only a single slash (\myfolder\blah).

Try this extension method:

public static bool IsUncPath(this string path)
{
    return Uri.TryCreate(path, UriKind.Absolute, out Uri uri) && uri.IsUnc;
}

The most accurate approach is going to be using some interop code from the shlwapi.dll

[DllImport("shlwapi.dll", CharSet = CharSet.Unicode)]
[ResourceExposure(ResourceScope.None)]
[return: MarshalAsAttribute(UnmanagedType.Bool)]
internal static extern bool PathIsUNC([MarshalAsAttribute(UnmanagedType.LPWStr), In] string pszPath);

You would then call it like this:

    /// <summary>
    /// Determines if the string is a valid Universal Naming Convention (UNC)
    /// for a server and share path.
    /// </summary>
    /// <param name="path">The path to be tested.</param>
    /// <returns><see langword="true"/> if the path is a valid UNC path; 
    /// otherwise, <see langword="false"/>.</returns>
    public static bool IsUncPath(string path)
    {
        return PathIsUNC(path);
    }

@JaredPar has the best answer using purely managed code.