From the Guidelines

Combining Nonsteroidal Anti-Inflammatory Drugs (NSAIDs) and Selective Serotonin Reuptake Inhibitors (SSRIs) increases the risk of bleeding.

The risk of bleeding is increased when NSAIDs are combined with other medications that affect platelet function, such as aspirin, but the evidence does not specifically address the combination of NSAIDs and SSRIs.
However, SSRIs have been associated with an increased risk of bleeding, particularly when combined with other medications that affect platelet function or coagulation [no specific reference provided in the evidence, but this is a well-established fact in clinical medicine].
The evidence provided focuses on the gastrointestinal risks of NSAIDs, including the increased risk of bleeding when NSAIDs are combined with aspirin or other medications that affect coagulation.
The risk of gastrointestinal bleeding with NSAIDs is increased by factors such as age, history of gastrointestinal events, and concomitant use of anticoagulation therapy or corticosteroids 1.
The use of COX-2-specific inhibitors may decrease the risk of gastrointestinal bleeding compared to non-selective NSAIDs, but the evidence does not address the specific combination of NSAIDs and SSRIs 1.

A study found that the combined use of NSAIDs and aspirin increases the risk of gastrointestinal bleeding to more than 10 times that seen among those using either NSAIDs or aspirin alone 1.
Another study found that the risk of gastrointestinal complications in NSAID users over the age of 65 years is increased approximately 2-3.5-fold when compared with younger patients 1.
The evidence suggests that proton pump inhibitors may decrease the risk of bleeding ulcers in high-risk NSAID or aspirin users, but it is unclear whether this would also apply to users of SSRIs 1.

Clinicians should exercise caution when prescribing NSAIDs to patients taking SSRIs, particularly if they have a history of gastrointestinal events or are taking other medications that affect coagulation.
Patients should be monitored closely for signs of bleeding, and alternative treatments should be considered if possible.
The use of COX-2-specific inhibitors or proton pump inhibitors may be considered to reduce the risk of gastrointestinal bleeding in patients taking NSAIDs and SSRIs, but the evidence is limited and more research is needed to fully understand the risks and benefits of these combinations.

From the Research

The concurrent use of Nonsteroidal Anti-Inflammatory Drugs (NSAIDs) and Selective Serotonin Reuptake Inhibitors (SSRIs) has been associated with an increased risk of bleeding, particularly gastrointestinal bleeding 2, 3, 4, 5.
A systematic review and meta-analysis found that the risk of upper gastrointestinal bleeding was increased with the use of SSRIs, and this risk was further increased when SSRIs were used in combination with NSAIDs (OR = 4.25,95% CI = 2.82-6.42) 2.
Another study found that the concurrent use of NSAIDs and SSRIs increased the risk of gastrointestinal bleeding compared to the use of NSAIDs alone (OR = 1.49,95% CI = 1.20-1.84) 3.
The risk of bleeding with concurrent NSAID and SSRI use has been found to be higher in patients with certain risk factors, such as a history of bleeding or acid-peptic disease 5.

A study comparing the bleeding risk of concomitant use of oral anticoagulants (OACs) and NSAIDs found that the risk of any bleeding and gastrointestinal bleeding was increased with the use of vitamin K antagonists (VKAs) and NSAIDs, as well as with the use of direct OACs (DOACs) and NSAIDs 6.
The risk of bleeding with concurrent use of DOACs and NSAIDs was found to be lower than with VKAs and NSAIDs in some studies (OR = 0.55,95% CI = 0.34-0.90) 6.
The risk of bleeding with SSRIs has been found to be increased when used in combination with other medications that affect platelet function, such as aspirin or anticoagulants 5.

Clinicians should exercise caution when prescribing NSAIDs and SSRIs concurrently, particularly in patients with a history of bleeding or other risk factors for bleeding 2, 3, 4, 5.
The use of proton pump inhibitors or other medications to reduce the risk of gastrointestinal bleeding may be considered in patients taking NSAIDs and SSRIs concurrently 5.
Further research is needed to fully understand the mechanisms of bleeding associated with SSRIs and to determine the best strategies for managing bleeding risk in patients taking these medications 5.