This is an answer from European perspective.
As @JanStuller has explained a retail cash deposit results in two balance sheet entries.
In the simplest form:
(Liability) Customer Demand Deposit, e.g. €100
(Asset) Central Bank Deposit, e.g. €100
Capital Requirements
The asset can be transformed to other forms but according to Capital Requirements Regulation Article 114 a cash deposit with the ECB has a risk weight of 0%. Therefore no additional capital is required to be held against this customer deposit on this measure.
$$ \text{new ratio} = \frac{\text{old capital}}{\text{old risk weighted assets + 0% x €100}} $$
Liquidity Coverage Ratio
Article 412 essentially states that liquid assets must cover outflows minus inflows over the next 30 days. Again the asset form is important but here 100% of the central bank deposit is counted, but the liability is only counted from 5% to 10%, as retail deposits are generally considered sticky Article 421 so there is a 'run-off' rate. This impacts the ratio favourably.
$$ \text{new ratio} = \frac{\text{old HQLA + 100% x €100}}{\text{old net outflows + 95% x €100}} $$
Net Stable Funding Ratio
This basically says that the available stable funding (ASF) exceeds the required stable funding. Basel states that demand deposits qualify for 90-95% ASF while central bank deposits amount to no RSF, so here again the ratio is impacted favourably.
$$ \text{new ratio} = \frac{\text{old ASF + 95% x €100}}{\text{old RSF outflows + 0% x €100}} $$
Leverage Ratio
This is a banks Tier 1 capital divided by total exposure. The exposure of a central bank deposit is zero (I believe) Article 11. Therefore in this scenario the ratio is unchanged.
$$ \text{new ratio} = \frac{\text{old capital}}{\text{old risk exposure + 0% x €100}} $$
Net Interest Income
The profit for the bank here is the interest rate differential between the central bank deposit and the retail deposit account. In Europe this is problematic since the central bank rate is lower than 0%.
Other factors
When that asset is not a central bank deposit it clearly impacts the above calculations. On top of that there may well be additional capital charges for market risk, i.e. if you buy a long dated treasury bond instead of T-bill.