Micrologix Analog input troublshooting

I there any easy way to determine if an analog input in a micrologix 1761 has gone bad?

I have checked the trasducer and it is working fine. The transducer is terminated on analog inputs IA/3 I(+) and IA(-).

I thought about using the multimeter as a 4 to 20mA source, but I am unsure how the PLC will react.

I'm not familiar with Micrologix analog. This answer is general 4-20 ma troubleshooting.
The input should have a 250 ohm resistor inside. This translates 4-20 ma into 1-5 volts. Do you have the card set to 4-20 ma? If it only has a 1-5 volt setting, then your need to add a 250 ohm (precision) resistor across the input terminals if your transducer is 4-20 ma.

When your transducer is putting out 4 ma, you should read 1 volt across the PLC Analog Input terminals. At 20 ma, it's 5 volts.
The 4 ma bottom limit is used as a fault detector. Significantly less than 1 volt means open circuit.
Measure voltage across the 2 input pins. You should read 1-5 volts. The meter won't affect the circuit.
Disconnect the transducer - do you get an open loop fault?
With the transducer disconnected, connect a 1.5 volt battery to the input. You should get a reading of about 6 ma.