Is it safe to make arduino read negative voltages from the analog inputs?
You cannot read negative voltages with the Atmel MCU on an Arduino board. They are only capable of reading positive voltages.

To solve your problem you need to design a positive referenced voltage divider or an op-amp circuit that includes scaling of the total delta voltage of the input to the min/max conversion range of the Atmel MCU. The circuit will also need to provide a DC offset to the input signal so that the resultant scaled output is centered within the conversion range of the A/D on the MCU.

If you use an op-amp circuit it could be necessary to provide a bipolar power supply depending upon the configuration of the op-amp circuit.

Note that the op-amp circuit can have a decided advantage over the simpler voltage divider circuit in that it can (a) offer a higher input impedance as a load to your analogue source and (b) is able to drive the A/D input of the MCU with a significantly lower source impedance. Both of these factors can lead to higher performance of the data conversion interface.