Grimes County reports three new COVID-19 cases Posted in: COVID-19News Grimes County Emergency Management released three new COVID-19 cases in Grimes County Wednesday, May 6, raising the total to 26. All three of the new cases released are males residing in the 77868 ZIP code outside the Navasota city limits. Case 24 is a male in his 50’s, case 25 is ...PLEASE LOG IN FOR PREMIUM CONTENT. Our website requires visitors to log in to view the best local news. Not yet a subscriber? Subscribe today!