I think, measurement of dependence of gain in laser active medium on pump power can shed the light. In 4 level gain must be linear. However, lasing at 1.064 hardly can be via 3 level in any host, while lasing at e.g. 946 nm will be closer to 3 level scheme in any host. Level scheme of lasing ion mostly determines the scheme 

I think, measurement of dependence of gain in laser active medium on pump power can shed the light. In 4 level gain must be linear. However, lasing at 1.064 hardly can be via 3 level in any host, while lasing at e.g. 946 nm will be closer to 3 level scheme in any host. Level scheme of lasing ion mostly determines the scheme 

3 level: GS is the lower state of laser transition.

4 level: GS is not lower state of laser  transition.

The first answer already states that the 4-level gain must be linear, whereas the 3-level is not (due to reabsorption the fluorescenses is amplified amongst other effects). However, this is difficult to see with only one laser, because all other experimental components may contribute noisily. Then, there is a certain chance to see the other lines, like, from the upper laser level to the ground state and from the upper pump level to the lower laser level. They are very weak and you will need a highly sensitive spetrograph for this, besides the filtering (which may be done with a grating..). Good luck, I still think about other solutions.

1.064 can be used as a "3-level-system" by directly pumping with 880nm. More on this: http://www.rp-photonics.com/four_level_and_three_level_gain_media.html

3- or 4-level scheme is a simplified model, convenient for calculations only. When we consider experiment to determine, which model can describe our laser better, we must take in mind real spectroscopic scheme of levels, temperature broadening, relaxation time, etc. For example, well known Nd3+ in YAG:  4F3/2 to 4I11/2: for CW or long pulses - 4-level, for short pulse amplification -3 level, due to relatively slow relaxation to ground state. Then, 4F3/2 to 4I9/2: at low temperature  -4- level, due to ground state splitting, but when temperature increases - turns into 3-level.

I agree with Aleksandr, however I remind you that the efficiency of 4 level system is usually higher than 3 level. If the laser  threshold is low and the inversion population takes place in low pumping energy, then the system is 4 level.

Check the laser efficiency and decide wether it is 3 or 4 level system or look at the energy diagram of laser transition and GS, that is another way  to find why it is the 3 or 4 level.

"Gain is linear in 4-level system" Alexandr wrote:

To which parameter is the gain linear? pumping rate, input intensity, or dopant concentration ?