Unfortunately, the AHT20 datasheet doesn't tell you how to do the data extraction. Here are the relevant code snippets I used:
TinyWireM.requestFrom(AHT20_ADDR,7); // Request 7 bytes from slave
state = TinyWireM.receive();
humi1 = TinyWireM.receive();
humi2 = TinyWireM.receive();
humitemp = TinyWireM.receive();
temp1 = TinyWireM.receive();
temp2 = TinyWireM.receive();
CRCdata = TinyWireM.receive();
unsigned long humi_1=humi1;
unsigned long humid = ((humi_1<<12)+(humi2<<4)+(humitemp>>4));
humidity=humid/10486.;
unsigned long humitemp_1=humitemp;
humitemp_1=humitemp_1&0x0F;
unsigned long temper = ((humitemp_1 <<16)+(temp1<<8)+(temp2));
temperature=(temper/1048576.)*200-50;