Not if you fairly evaluate their performance and treat them consistently. It is common for employees who have performance concerns to lodge complaints against their managers around performance evaluation time. Complaints may arise by as much as one-third during evaluation periods. Such employees allege they have been set up to fail by their managers due to their race, gender, or other discriminatory reason or on account of personal dislike (not a legally protected factor). For some employees, this may be true and for others, this is a preemptive excuse for performing poorly.
Although an ongoing complaint makes it awkward for the manager to evaluate an employee's performance and manage them day-to-day, it can indeed be done if the manager sets aside emotions and just sticks to the business-related facts at hand. Stay focused on the task before you.
Understand that the employee is responsible for his or her own performance and you are responsible for simply EVALUATING that performance. Hopefully, you have done the following as a manager:
1) adopted pre-established performance objectives that were discussed with the employee and agreed to at the beginning of the evaluation period
2) used multiple data sources for your evaluations (e.g., productivity numbers, qualitative judgments by customers, peers, managers, etc.
3) provided timely and appropriate feedback (rather than saving it up for the end of the year) -- there should be NO SURPRISES
4) kept a log of critical performance incidents, both positive and negative, throughout the year so you can provide examples of problematic and good behavior
5) held semi-formal periodic performance check-ins throughout the year (e.g., quarterly or at least the half-year mark)
6) kept upper management aware of the performance concerns and how you have been addressing them
7) provided appropriate resources, training, and direction to accomplish the objectives.
Don't be afraid to draft the performance document and partner with your management and HR for a review of the document and guidance on delivering feedback to the employee. Make sure you communicate that you are interested in continuing to treat the employee fairly and consistently and that given their complaint against you, you think it is appropriate to have another set of eyes. It's harder for the employee to claim retaliation if you gain advance agreement from these parties.
Good luck. You should be okay if you follow these parameters.