Statement 1 : Ionisation energy decreases in a period.

Statement 2 : In a period Z dominates over screening effect

Let us analyze both statements step-by-step to understand the behavior of periodic properties across a period.

Analysis of Statement 1: Ionisation energy decreases in a period.
Ionization energy is the minimum amount of energy required to remove the most loosely bound electron from an isolated gaseous atom. As we move from left to right across a period in the periodic table:
1. The principal quantum number ($n$) remains the same, meaning electrons are added to the same outermost shell.
2. The number of protons in the nucleus increases, which increases the nuclear charge ($Z$).
3. The effective nuclear charge ($Z_{\text{eff}}$) acting on the valence electrons increases.
4. Consequently, the atomic radius decreases, and the valence electrons are pulled more strongly by the nucleus.
Because the electrostatic pull on the outer electrons becomes stronger, it requires more energy to remove an electron. Therefore, ionization energy generally increases across a period from left to right. This makes Statement 1 incorrect.

Analysis of Statement 2: In a period Z dominates over screening effect.
As we move across a period, both the nuclear charge ($Z$) and the number of shielding (screening) electrons increase. However, the new electrons are added to the same main energy level, which does not screen the outer electrons very effectively compared to inner shell electrons. As a result, the increase in nuclear charge ($Z$) outweighs the small increase in the screening effect ($\sigma$). Thus, the effective nuclear charge:
$Z_{\text{eff}}=Z-\sigma$
increases across the period because the increase in $Z$ dominates over $\sigma$. Therefore, Statement 2 is correct.

Conclusion:
Statement 1 is incorrect, and Statement 2 is correct.