Yes, in many cases, you may reapply. If you reapply, you will need to complete and resubmit a new Form N-400, Application for Naturalization, and pay the fee again. You will also need to have your fingerprints and photographs taken again. If your application is denied, the denial letter should indicate the date you may reapply for Citizenship. If you are denied because you failed the English or Civics test, you may reapply for Naturalization as soon as you want. You should reapply whenever you believe you have learned enough English or Civics to pass the test.
You may get a new Certificate of Naturalization by submitting Form N-565, Application for Replacement Naturalization/Citizenship Document, to the USCIS if you have lost your Certificate of Naturalization. It may take up to one year for you to receive a new certificate.