Despite having a relatively large population just over 22,000 as of the 2008 census report (which you can access for yourself at https://www.census.gov/programs-surveys/popest.html ), Limestone County has a rather low prisoner population of just 214 prisoners (as of the TDCJ report at https://www.tdcj.state.tx.us/documents/Statistical_Report_FY2014.pdf ).
However, just because crime appears to be relatively low in Limestone County doesnt mean that you shouldnt be very careful when it comes to hiring new employees and babysitters. In fact, whenever you form any sort of new contact, it is highly advisable that you at least perform a cursory search to see where they stand legally.
Your best bet to begin an arrest warrant search for Limestone County, Texas is right through the Limestone County Sheriffs Office. Located at 1221 E. Yeagua Street in Groesbeck, Texas 76642, you can also reach them via telephone at 254-729-3278.
If you would like to search through the arrest records of all of the persons currently serving time in the Texas prison system, you may do so at https://offender.tdcj.texas.gov/OffenderSearch/index.jsp . Simply enter in all of the information that you happen to have, and let the search engine do the rest.