Identify the species:

The compound is nitric oxide, $\mathrm{NO}$.

Check each option:

Option A: It combines with oxygen to form nitrogen dioxide

This is true. $2\mathrm{NO} + \mathrm{O}_2 \rightarrow 2\mathrm{NO}_2$ So NO does combine with oxygen to form $\mathrm{NO}_2$.

Option B: Its bond order is $2.5$

This is also true.

Total valence electrons in NO: $5 + 6 = 11$ Since NO has an odd number of electrons, it is a radical. From molecular orbital theory, NO has bond order: $\text{Bond order} = \frac{N_b - N_a}{2} = 2.5$ So this statement is correct.

Option C: It is diamagnetic in gaseous state

This is false.

NO has 11 valence electrons, so one electron remains unpaired in the molecular orbital configuration. Therefore, NO is paramagnetic, not diamagnetic.

Option D: It is a neutral oxide

This is true.

NO is classified as a neutral oxide because it is neither acidic nor basic under normal conditions.

Conclusion:

The property not shown by NO is: $\boxed{\text{C}}$

because NO is paramagnetic, not diamagnetic.