No one can absolutely answer that question for you, but here is a tool to help you make your decision.

Look at the matter

(1 point)

(2 points)

(3 points)

The matter to be investigated is

Simple, involving two parties and one or two

Moderate in Complexity, involving more than
two parties or multiple incidents

High in complexity, involving multiple
parties and multiple incidents, or
allegations of hostile environment

The person(s) accused of misconduct

Are non managerial and at the same rank as
the complainant

Are middle management
higher in rank than the complainant

Are senior managers or executives

The complaints involve

Inappropriate language, jokes or simple

A combination of inappropriate language and
multiple acts of misconduct

Extreme racial, sexual or
threatening/harassing behavior

The person to do the investigating

Is extremely experienced and confident

Has some experience, but is uncertain about
the best way to proceed

Is inexperienced OR is in a reporting
relationship to a party in the investigation

1-4: Almost certainly manageable internally
5-9: Consider using outside investigator
10: Recommend outside investigator