It is the mode of attack that determines the stereospecificity. In the reaction of singlet carbene the pi orbitals are involved in bonding with the p-orbital which contains the lone pair and it forms a complex and which does not disturb the stereochemistry of the original comound. Whereas in the triplet reaction since it has 1 electron each in 2 orbitals if first attacks the first carbon creating a carbocation which then destroys the stereospecificity.

 

Example:

cis-2-butene + :CH2(singlet) --> cis-1,2-dimethyl cyclopropane

cis-2-butene + :CH2(triplet) ---> cis- + trans-(50% and 50%).