Temperature dependent current voltage (I-V) characteristics, capacitance-voltage (C-V), conductance-voltage (G-V), frequency dependent capacitance for understanding the dielectric properties are the basic measurements you can go for. Also, few advanced measurements including current transient, voltage sweep in cycles of +ve and -ve polarities would provide the possibility towards new applications.
You can sandwich the thin film of nanoparticles between two electrodes and go for the C-V measurements of various flavours with frequency and voltage dependences, using LCR/capacitance meter. Also, you can use an external voltage source if you need higher voltages or if you use a capacitance meter. You can search the literatures/ books to perform the capacitance-voltage experiments in the lab.