Dana Rosu, from Aberdeen, appeared in private at the city's Sheriff Court in relation to a charge of breach of the peace on the Safe Scandinavia platform.
Ms Rosu made no plea or declaration and was remanded to Cornhill Hospital in Aberdeen for assessment.
A total of 161 staff were airlifted from the installation during the alert on Sunday.
The evacuation came after allegations of a "possible suspicious device".
Britannia Operator Ltd, which owns the installation, confirmed the workers had returned to the platform having been moved to neighbouring rigs while investigations were carried out.
The company's managing director, Kathy McGill, added: "We are very relieved that this has turned out to be a false alarm, but we obviously had to treat it seriously and act appropriately to ensure the safety and wellbeing of all our people."
The Safe Scandinavia, an accommodation installation attached by a bridge to an oil rig in the Britannia field, lies 130 miles off the Aberdeen coast.
Source: BBC News