No damage or injuries have been reported.
KDFW-TV reported Friday that State Farm recently mailed letters to residents recommending they add earthquake insurance to their homeowner policies.
City officials and residents wonder whether natural gas drilling could be a factor. Seismographs have been installed in Cleburne.
Earthquakes had never surfaced in Cleburne, a city of about 22,000 located 50 miles southwest of Dallas, until last month.
The last one was July 10. The U.S. Geological Survey-recorded 2.0-magnitude quake.
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