The first incident occurred days after Geldof's death, when someone stole a lawnmower from house grounds.
Police are also investigating a break-in that took place on Friday. Officers arrived at the house to find that CCTV footage had been damaged, though nothing appeared to be stolen.
"Police are investigating a burglary at an address in Fairseat Lane, Wrotham, on 9 May," they said in a statement. "Officers were at the address within five minutes and no personal items are believed to have been stolen."
Cohen found his wife, daughter of rocker Bob Geldof and late British TV presenter Paula Yates, dead in a spare bedroom last month.