Checking from the registry may not work all the time becasue if user uninstall the localDb then registry entries may still exist.
Here is the function I am using to identify the localDB installation from command line -
internal static bool IsLocalDBInstalled()
{
// Start the child process.
Process p = new Process();
// Redirect the output stream of the child process.
p.StartInfo.UseShellExecute = false;
p.StartInfo.RedirectStandardOutput = true;
p.StartInfo.FileName = "cmd.exe";
p.StartInfo.Arguments = "/C sqllocaldb info";
p.StartInfo.CreateNoWindow = true;
p.StartInfo.WindowStyle = System.Diagnostics.ProcessWindowStyle.Hidden;
p.Start();
// Do not wait for the child process to exit before
// reading to the end of its redirected stream.
// p.WaitForExit();
// Read the output stream first and then wait.
string sOutput = p.StandardOutput.ReadToEnd();
p.WaitForExit();
//If LocalDb is not installed then it will return that 'sqllocaldb' is not recognized as an internal or external command operable program or batch file.
if (sOutput == null || sOutput.Trim().Length == 0 || sOutput.Contains("not recognized"))
return false;
if (sOutput.ToLower().Contains("mssqllocaldb")) //This is a defualt instance in local DB
return true;
return false;
}