Understanding Touch Switch with BJTs and Relay
This is a bit of a creepy circuit. It appears to work on the relay hysteresis. So the relay coil, in series with a diode D2 and the 100\$\Omega\$ resistor, receives enough current to hold the relay in, but not to actuate it. 

Full voltage is applied to the relay when TP1 is bridged, so it pulls in. 

When TP2 is bridged, the 100\$\Omega\$ resistor receives current from the Darlington pair T2/T3 and the relay current drops to a very low level, so it drops out. 

May require fiddling depending on the relay characteristics etc. A sharp tap on the relay when it is pulled in (without TP1 bridged) may cause it to drop out. Similarly, a sharp tap when de-energized could cause it to pull in (but that would take a lot more of a whack).