To determine the correct answer from the provided options, we need to analyze the accuracy of both statements based on our understanding of the Hofmann degradation reaction.
Statement I: "In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom."
This statement is incorrect. In the Hofmann degradation reaction, an amide reacts with bromine in an aqueous or alcoholic solution of sodium hydroxide to form a primary amine with one fewer carbon atom. The crucial point is that the migration step involves the removal of the carbonyl group, and the rearrangement occurs such that the amine product has one less carbon atom than the original amide. The alkyl group does not migrate to the nitrogen atom as suggested; instead, it’s the nitrogen that effectively receives an extra carbon, shortening the chain.
Statement II: "The group is migrated in Hofmann degradation reaction to electron deficient atom."
This statement is correct. In the reaction mechanism, there is a migration of an alkyl group that effectively happens towards an electron-deficient atom (the nitrogen atom becomes part of a more significant electron deficit due to the loss of the carbonyl group). This migration makes the nitrogen atom possess the extra alkyl group, as electron migration dynamics dictate such behavior.
Given this understanding, the correct answer is: Statement I is incorrect but Statement II is correct.
To summarize:

